representation of orthogonal group

www.springer.com The European Mathematical Society

• StatProb Collection
• Recent changes
• Current events
• Random page
• Project talk
• Request account
• What links here
• Related changes
• Special pages
• Printable version
• Permanent link
• Page information
• View source

Representation of the classical groups

Linear representations (cf. Linear representation ) of the groups $ \mathop{\rm GL} ( V) $, $ \textrm{SL} ( V) $, $ \textrm{O} ( V, f ) $, $ \textrm{SO} ( V, f ) $, $ \textrm{Sp} ( V, f ) $, where $ V $ is an $ n $-dimensional vector space over a field $ k $ and $ f $ is a non-degenerate symmetric or alternating bilinear form on $ V $, in invariant subspaces of tensor powers $ T ^ {m} ( V) $ of $ V $. If the characteristic of $ k $ is zero, then all irreducible polynomial linear representations of these groups can be realized by means of tensors.

In the case $ k = \mathbf C $ the groups above are complex Lie groups. For all groups, except $ \textrm{GL} ( V) $, all (differentiable) linear representations are polynomial; every linear representation of $ \textrm{ GL} ( V) $ has the form $ g \mapsto ( \det g) ^ {k} R ( g) $, where $ k \in \mathbf Z $ and $ R $ is a polynomial linear representation. The classical compact Lie groups $ \textrm{U} _ {n} $, $ \textrm{SU} _ {n} $, $ \textrm{O} _ {n} $, $ \textrm{SO} _ {n} $, and $ \textrm{Sp} _ {n} $ have the same complex linear representations and the same invariant subspaces in tensor spaces as their complex envelopes $ \textrm{U} _ {n} ( \mathbf C ) $, $ \textrm{SL} _ {n} ( \mathbf C ) $, $ \textrm{O} _ {n} ( \mathbf C ) $, $ \textrm{SO} _ {n} ( \mathbf C ) $, and $ \textrm{Sp} _ {n} ( \mathbf C ) $. Therefore, results of the theory of linear representations obtained for the classical complex Lie groups can be carried over to the corresponding compact groups and vice versa (Weyl's "unitary trick" ). In particular, using integration on a compact group one can prove that linear representations of the classical complex Lie groups are completely reducible.

The natural linear representation of $ \textrm{GL} ( V) $ in $ T ^ {m} ( V) $ is given by the formula

$$ g ( v _ {1} \otimes \dots \otimes v _ {m} ) = \ gv _ {1} \otimes \dots \otimes gv _ {m} ,\ \ g \in \textrm{GL} ( V),\ \ v _ {i} \in V. $$

In the same space a linear representation of the symmetric group $ S _ {m} $ is defined by

$$ \sigma ( v _ {1} \otimes \dots \otimes v _ {m} ) = \ v _ {\sigma ^ {- 1 }( 1) } \otimes \dots \otimes v _ {\sigma ^ {- 1 }( m) } ,\ \ \sigma \in S _ {m} ,\ \ v _ {i} \in V. $$

The operators of these two representations commute, so that a linear representation of $ \textrm{GL} ( V) \times S _ {m} $ is defined in $ T ^ {m} ( V) $. If $ \mathop{\rm char} k = 0 $, the space $ T ^ {m} ( V) $ can be decomposed into a direct sum of minimal $ ( \textrm{GL} ( V) \times S _ {m} ) $-invariant subspaces:

$$ T ^ {m} ( V) = \ \sum _ \lambda V _ \lambda \otimes U _ \lambda . $$

The summation is over all partitions $ \lambda $ of $ m $ containing at most $ n $ summands, $ U _ \lambda $ is the space of the absolutely-irreducible representation $ T _ \lambda $ of $ S _ {m} $ corresponding to $ \lambda $ (cf. Representation of the symmetric groups ) and $ V _ \lambda $ is the space of an absolutely-irreducible representation $ R _ \lambda $ of $ \textrm{GL} ( V) $. A partition $ \lambda $ can be conveniently represented by a tuple $ ( \lambda _ {1} \dots \lambda _ {n} ) $ of non-negative integers satisfying $ \lambda _ {1} \geq \dots \geq \lambda _ {n} $ and $ \sum _ {i} \lambda _ {i} = m $.

The subspace $ V _ \lambda \otimes U _ \lambda \subset T ^ {m} ( V) $ splits in a sum of minimal $ \textrm{GL} ( V) $-invariant subspaces, in each of which a representation $ R _ \lambda $ can be realized. These subspaces can be explicitly obtained by using Young symmetrizers (cf. Young symmetrizer ) connected with $ \lambda $. E.g. for $ \lambda = ( m, 0 \dots 0) $ (respectively, $ \lambda = ( 1 \dots 1, 0 \dots 0) $ for $ m \leq n $) one has $ \dim U _ \lambda = 1 $ and $ V _ \lambda \otimes U _ \lambda $ is the minimal $ \textrm{GL} ( V) $-invariant subspace consisting of all symmetric (respectively, skew-symmetric) tensors.

The representation $ R _ \lambda $ is characterized by the following properties. Let $ B \subset \textrm{GL} ( V) $ be the subgroup of all linear operators that, in some basis $ \{ e _ {1} \dots e _ {n} \} $ of $ V $, can be written as upper-triangular matrices. Then the operators $ R _ \lambda ( b) $, $ b \in B $, have a unique (up to a numerical factor) common eigenvector $ v _ \lambda $, which is called the highest weight vector of $ R _ \lambda $. The corresponding eigenvalue (the highest weight of $ R _ \lambda $) is equal to $ b _ {11} ^ {\lambda _ {1} } \dots b _ {nn} ^ {\lambda _ {n} } $, where $ b _ {ii} $ is the $ i $-th diagonal element of the matrix of $ b $ in the basis $ \{ e _ {1} \dots e _ {n} \} $. Representations $ R _ \lambda $ corresponding to distinct partitions $ \lambda $ are inequivalent. The character of $ R _ \lambda $ can be found from Weyl's formula

$$ \tr R _ \lambda ( g) = \ \frac{W _ \lambda ( z _ {1} \dots z _ {n} ) }{W _ {0} ( z _ {1} \dots z _ {n} ) } , $$

where $ z _ {1} \dots z _ {n} $ are the roots of the characteristic polynomial of the operator $ g $, $ W _ \lambda $ is the generalized Vandermonde determinant corresponding to $ \lambda $ (cf. Frobenius formula ) and $ W _ {0} $ is the ordinary Vandermonde determinant. The dimension of $ R _ \lambda $ is equal to

$$ \dim R _ \lambda = \ \prod _ {i < j } \frac{l _ {i} - l _ {j} }{j - i } , $$

where $ l _ {i} = \lambda _ {i} + n - i $.

The restriction of $ R _ \lambda $ to the unimodular group $ \textrm{SL} ( V) $ is irreducible. The restrictions to $ \textrm{SL} ( V) $ of two representations $ R _ \lambda $ and $ R _ \mu $ are equivalent if and only if $ \mu _ {i} = \lambda _ {i} + s $ (where $ s $ is independent of $ i $). The restriction of a representation $ R _ \lambda $ of $ \textrm{GL} _ {n} ( k) $ to the subgroup $ \textrm{GL} _ {n - 1 } ( k) $ can be found by the rule:

$$ R _ \lambda \mid _ { \textrm{GL} _ {n - 1 } ( k) } = \ \sum _ \mu R _ \mu , $$

where $ \mu $ runs through all tuples $ ( \mu _ {1} \dots \mu _ {n - 1 } ) $ satisfying

$$ \lambda _ {1} \geq \mu _ {1} \geq \ \lambda _ {2} \geq \mu _ {2} \geq \dots \geq \lambda _ {n} . $$

For every Young diagram $ d $, corresponding to a partition $ \lambda $, the tensor $ v _ \lambda \otimes u _ {d} ^ \prime \in T ^ {m} ( V) $ (for notations see Representation of the symmetric groups ) is the result of alternating the tensor $ e _ {i _ {1} } \otimes \dots \otimes e _ {i _ {m} } $ over the columns of $ d $, where $ i _ {k} $ is the number of the row of $ d $ in which the number $ k $ is located. The tensors thus constructed with respect to all standard diagrams $ d $ form a basis of the minimal $ S _ {m} $-invariant subspace of $ v _ \lambda \otimes U _ \lambda $ in which the representation $ T _ \lambda $ of $ S _ {m} $ is realized.

A linear representation of the orthogonal group $ \textrm{O} ( V, f ) $ in $ T ^ {m} ( V) $ has the following structure. There is a decomposition into a direct sum of two $ ( \textrm{O} ( V, f ) \times S _ {m} ) $-invariant subspaces:

$$ T ^ {m} ( V) = T _ {0} ^ {m} ( V) \oplus T _ {1} ^ {m} ( V) , $$

where $ T _ {0} ^ {m} ( V) $ consists of traceless tensors, i.e. tensors whose convolution with $ f $ over any two indices vanishes, and

$$ T _ {1} ^ {m} ( V) = \ \sum _ {\sigma \in S _ {m} } \sigma ( T ^ {m - 2 } ( V) \otimes f ^ { - 1 } ). $$

The space $ T _ {0} ^ {m} ( V) $, in turn, decomposes into a direct sum of $ ( \textrm{O} ( V, f ) \times S _ {m} ) $-invariant subspaces:

$$ T _ {0} ^ {m} ( V) = \ \sum _ \lambda V _ \lambda ^ {0} \otimes U _ \lambda , $$

where $ V _ \lambda ^ {0} \subset V _ \lambda $. Moreover, $ V _ \lambda ^ {0} \neq 0 $ if and only if the sum $ \lambda _ {1} ^ \prime + \lambda _ {2} ^ \prime $ of the heights of the first two columns of the Young tableau corresponding to $ \lambda $ does not exceed $ n $, and in this case $ V _ \lambda ^ {0} $ is the space of an absolutely-irreducible representation $ R _ \lambda ^ {0} $ of $ \textrm{O} ( V, f ) $. Representations $ R _ \lambda ^ {0} $ corresponding to distinct partitions $ \lambda $ are inequivalent. If $ \lambda $ satisfies the condition $ \lambda _ {1} ^ \prime + \lambda _ {2} ^ \prime \leq n $, then after replacing the first column of its Young tableau by a column of height $ n - \lambda _ {1} ^ \prime $ one obtains the Young tableau of a partition $ \overline \lambda $ which also satisfies this condition. The corresponding representations of $ \textrm{O} ( V, f ) $ are related by $ R _ {\overline \lambda } ^ {0} ( g) = ( \det g) R _ \lambda ^ {0} ( g) $ (in particular, they have equal dimension).

The restriction of $ R _ \lambda ^ {0} $ to the subgroup $ \textrm{SO} ( V, f ) $ is absolutely irreducible, except in the case $ n $ even and $ \lambda = \overline \lambda $ (i.e. the number of terms of $ \lambda $ is equal to $ n/2 $). In the latter case it splits over the field $ k $ or a quadratic extension of it into a sum of two inequivalent absolutely irreducible representations of equal dimension.

In computing the dimension of $ R _ \lambda ^ {0} $ one can assume that $ \lambda _ {1} ^ \prime \leq n/2 $ (otherwise replace $ \lambda $ by $ \overline \lambda $). Let $ l _ {i} = \lambda _ {i} + n/2 - i $. Then for odd $ n $ one has

$$ \dim R _ \lambda ^ {0} = \ \prod _ {i = 1 } ^ { [ n/2]} \frac{l _ {i} }{n/2 - i } \prod _ {\begin{array}{c} i, j = 1 \\ i < j \end{array} } ^ { [ n/2]} \frac{( l _ {i} - l _ {j} ) ( l _ {i} + l _ {j} ) }{( j - i) ( n - i - j) } , $$

while for even $ n $ and $ \lambda \neq \overline \lambda $ one has

$$ \dim R _ \lambda ^ {0} = \ \prod _ {\begin{array}{c} i, j = 1 \\ i < j \end{array} } ^ { n/2 } \frac{( l _ {i} - l _ {j} ) ( l _ {i} + l _ {j} ) }{( j - i) ( n - i - j) } . $$

For $ \lambda = \overline \lambda $ the latter formula gives half the dimension of $ R _ \lambda ^ {0} $, i.e. the dimension of each of the absolutely-irreducible representations of $ \textrm{SO} ( V, f ) $ corresponding to it.

The decomposition of $ T ^ {m} ( V) $ with respect to the symplectic group $ \textrm{Sp} ( V, f ) $ is analogous to the decomposition with respect to the orthogonal group, with the difference that $ V _ \lambda ^ {0} \neq 0 $ if and only if $ \lambda _ {1} ^ \prime \leq n/2 $. The dimension of $ R _ \lambda ^ {0} $ can in this case be found from

$$ \dim R _ \lambda ^ {0} = \ \prod _ {i = 1 } ^ { n/2 } \frac{l _ {i} }{n/2 - i + 1 } \prod _ {\begin{array}{c} i, j = 1 \\ i < j \end{array} } ^ { n/2 } \frac{( l _ {i} - l _ {j} ) ( l _ {i} + l _ {j} ) }{( j - i) ( n - j - i + 2) } , $$

where $ l _ {i} = \lambda _ {i} - i + 1 + n/2 $.

This article describes the classical theory. The contemporary period in this old field of algebra began with [a1] . It can be described by two words: "characteristic-free representation theory" . A different approach to the polynomial representations of $ \textrm{GL} ( V) $ and $ \textrm{SL} ( V) $ was undertaken in [a2] . Further, both classical and characteristic free theories can be found in [a3] .

• This page was last edited on 5 May 2022, at 08:00.
• Privacy policy
• About Encyclopedia of Mathematics
• Disclaimers
• Impressum-Legal

Orthogonal Group Representations

Explore with wolfram|alpha.

More things to try:

• battle of the sexes
• complexity class BPP
• inverse {{a, b}, {c, d}}

Cite this as:

Weisstein, Eric W. "Orthogonal Group Representations." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/OrthogonalGroupRepresentations.html

Subject classifications

• Previous Article
• Next Article

Representations of the Orthogonal Group. II. Polynomial Bases for the Irreducible Representations of the Orthogonal Group

• Article contents
• Figures & tables
• Supplementary Data
• Peer Review
• Reprints and Permissions
• Cite Icon Cite
• Search Site

M. K. F. Wong; Representations of the Orthogonal Group. II. Polynomial Bases for the Irreducible Representations of the Orthogonal Group. J. Math. Phys. 1 June 1969; 10 (6): 1065–1068. https://doi.org/10.1063/1.1664935

Download citation file:

• Ris (Zotero)
• Reference Manager

Polynomial bases for the irreducible representations of the orthogonal group, which are characterized by the Gel'fand pattern, have been obtained. The method used is very similar to Moshinsky's and is a generalization from the unitary group to the orthogonal group. The Wigner coefficients of O (3), commonly called the Clebsch‐Gordan coefficients of R (3), are rederived by means of the polynomial bases obtained in this paper.

Sign in via your Institution

Citing articles via, submit your article.

Sign up for alerts

• Online ISSN 1089-7658
• Print ISSN 0022-2488
• For Researchers
• For Librarians
• For Advertisers
• Our Publishing Partners  
• Physics Today
• Conference Proceedings
• Special Topics

pubs.aip.org

• Privacy Policy
• Terms of Use

Connect with AIP Publishing

This feature is available to subscribers only.

Sign In or Create an Account

Hermitian self-orthogonal matrix product codes and their applications to quantum codes

• Published: 15 March 2024
• Volume 23 , article number  108 , ( 2024 )

Cite this article

• Xiaoyan Zhang 1  

69 Accesses

Explore all metrics

In this paper, we propose a construction of quantum codes from Hermitian self-orthogonal matrix product codes over the finite fields. This construction is applied to obtain numerous new quantum codes, and all of them have higher rate than current quantum codes available.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

Dual Integrable Representations on Locally Compact Groups

Hrvoje Šikić & Ivana Slamić

Several families of MDS QECCs and MDS EAQECCs from Hermitian self-orthogonal GRS codes

Yang Li, Shixin Zhu & Yanhui Zhang

New Binary Quantum Codes from Group Rings and Skew Group Rings

Cong Yu & Shixin Zhu

Aly, S.A., Klappenecker, A., Sarvepalli, P.K.: On quantum and classical BCH codes. IEEE Trans. Inf. Theory 53 (3), 1183–1188 (2007)

Article   MathSciNet   Google Scholar  

Ashikhmin, A., Knill, E.: Nonbinary quantum stabilizer codes. IEEE Trans. Inf. Theory 47 (7), 3065–3072 (2001)

Blackmore, T., Norton, G.H.: Matrix-product codes over \(\mathbb{F} _q\) . Appl. Algebra Eng. Commun. Comput. 12 , 477–500 (2001)

Article   Google Scholar  

Bag, T., Dinh, H., Upadhyay, A., Bandi, R., Yamaka, W.: Quantum codes from skew constacyclic codes over the ring \(\mathbb{F} _q[u, v]/\langle u^2-1, v^2-1, uv-vu\rangle \) . Discrete Math. 343 , 111737 (2020)

Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over \(GF(4)\) . IEEE Trans. Inf. Theory 44 , 1369–1387 (1998)

Cao, M., Wang, H., Cu, J.: Construction of quantum codes from matrix-product codes. IEEE Commun. Lett. 24 (4), 706–710 (2020)

Cannon, J., Playoust, C.: An Introduction to Magma. The University of Sydney, Sydney (1994)

Google Scholar  

Galindo, C., Hernando, F., Ruano, D.: New quantum codes from evaluation and matrix-product codes. Finite Fields Their Appl. 36 , 98–120 (2015)

Jin, L., Ling, S., Luo, J., Xing, C.: Application of classical Hermitian self-orthogonal MDS codes to quantum MDS codes. IEEE Trans. Inf. Theory 56 (9), 4735–4740 (2010)

Jin, L., Xing, C.: A construction of new quantum MDS codes. IEEE Trans. Inf. Theory 60 (5), 2921–2925 (2014)

La Guardia, G.G.: Quantum Error Correction. Springer, Berlin (2020)

Book   Google Scholar  

Liu, X.S., Dinh, H.Q., Liu, H., Yu, L.: On new quantum codes from matrix product codes. Cryptogr. Commun. 10 (4), 579–589 (2018)

Article   ADS   MathSciNet   Google Scholar  

Liu, X.S., Yu, L., Hu, P.: New entanglement-assisted quantum codes from \(k\) -Galois dual codes. Finite Field Appl. 55 , 21–32 (2019)

Ma, F., Cao, J.: New non-binary quantum codes from constacyclic codes over \(\mathbb{F} _q[u, v]/\langle u^2-1, v^2-v, uv-vu\rangle \) . Adv. Math. Commun. 13 (3), 421–434 (2019)

Steane, A.M.: Multiple-particle interference and quantum error correction. Phys. Proc. Math. Phys. Eng. Sci. 452 (1954), 2551–2577 (1996)

Sok, L.: New families of quantum stabilizer codes from Hermitian self-orthogonal algebraic geometry codes. arXiv:2110.00769v1

Verma, R.K., Prakash, O., Singh, A., Islam, H.: New quantum codes from skew constacyclic codes. Adv. Math. Commun. (2021). https://doi.org/10.3934/amc.2021028

Zhang, T., Ge, G.: Quantum codes from generalized Reed–Solomon codes and matrix-product codes. arXiv:1508.00978v1

Download references

Acknowledgements

This work was supported by Research Funds of Hubei Province, Grant No. D20144401.

Author information

Authors and affiliations.

School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, Hubei, China

Xiaoyan Zhang

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Xiaoyan Zhang .

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Zhang, X. Hermitian self-orthogonal matrix product codes and their applications to quantum codes. Quantum Inf Process 23 , 108 (2024). https://doi.org/10.1007/s11128-024-04314-z

Download citation

Received : 03 May 2023

Accepted : 12 February 2024

Published : 15 March 2024

DOI : https://doi.org/10.1007/s11128-024-04314-z

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Quantum codes
• Matrix product codes
• Hermitian self-orthogonal

Mathematics Subject Classification

• Find a journal
• Publish with us
• Track your research

Help | Advanced Search

Mathematical Physics

Title: sister celine's polynomials in the quantum theory of angular momentum.

Abstract: The polynomials introduced by Sister Celine cover different usual orthogonal polynomials as special cases. Among them, the Jacobi and discrete Hahn polynomials are of particular interest for the quantum theory of angular momentum. In this note, we show that characters of irreducible representations of the rotation group as well as Wigner rotation "d" matrices, can be expressed as Sister Celine's polynomials. Since many relations were proposed for the latter polynomials, such connections could lead to new identities for quantities important in quantum mechanics and atomic physics.

Submission history

Access paper:.

• HTML (experimental)
• Other Formats

References & Citations

• INSPIRE HEP
• Google Scholar
• Semantic Scholar

BibTeX formatted citation

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

• Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

• Victor Mukhin

Victor M. Mukhin was born in 1946 in the town of Orsk, Russia. In 1970 he graduated the Technological Institute in Leningrad. Victor M. Mukhin was directed to work to the scientific-industrial organization "Neorganika" (Elektrostal, Moscow region) where he is working during 47 years, at present as the head of the laboratory of carbon sorbents.     Victor M. Mukhin defended a Ph. D. thesis and a doctoral thesis at the Mendeleev University of Chemical Technology of Russia (in 1979 and 1997 accordingly). Professor of Mendeleev University of Chemical Technology of Russia. Scientific interests: production, investigation and application of active carbons, technological and ecological carbon-adsorptive processes, environmental protection, production of ecologically clean food.   

Title : Active carbons as nanoporous materials for solving of environmental problems

Quick links.

• Conference Brochure
• Tentative Program

‘Total Disgrace’: Anger, Frustration as Mass Heating Failures Across Russia Leave Thousands in the Cold

P ODOLSK, Moscow region – Residents throughout Russia affected by unprecedented winter heating outages in recent days have expressed their frustration and urged local authorities to restore heating in their homes.

In Podolsk, a town some 30 kilometers south of the capital Moscow, at least 149,000 residents — nearly half of its population — were left without heating when a heating main burst at a nearby private ammunition plant.

“It’s a total disgrace. There is no heating and no hot water. We have to sleep in sleeping bags,” Yuri, a local resident, told The Moscow Times.

“I have no words to describe how bad the situation is," said Yuri, who declined to provide his surname. "We have had no heating for almost six days."

Heating issues have affected residents in the Moscow region, where temperatures have plunged to as low as minus 20 degrees Celsius in the past week, as well as people in the Far East Primorye region , the cities of Moscow and St. Petersburg , Penza , the southern Voronezh and Volgograd regions and more.

In the Tver region, a group of residents filmed an appeal to President Vladimir Putin, saying that they “are freezing from the cold” in the village of Novozavidovsky.

“We're literally being killed by the cold,” a woman in the video said, adding that they have been sending requests to local authorities since September after their houses were connected to a boiler room whose power was reportedly insufficient.

“This is some kind of torture and extermination of the population 100 kilometers from Moscow,” she added.

Residents of the Moscow region town of Elektrostal lit a fire in the street to draw the authorities’ attention to the heating problem.

“It’s impossible to stay in our houses. We're freezing!” a group of women in the video said.

Suffering from subzero temperatures, residents are placing the blame on local authorities and utility services for failing to take necessary precautions and not taking action to resolve the situation.

“We are sending complaints everywhere but no one listens to us. We have portable heaters working in every room, but the temperature inside is still 10 degrees Celsius,” Yelena from Podolsk said.

“There is a clinic and a hospital, as well as kindergartens, where there is no heating. And we have no answers, no assistance, no explanation,” Yelena added.

Podolsk authorities opened temporary heating centers and declared a state of emergency.

Local authorities linked the heating problems to the fact that the town is heated by a boiler plant owned by the Klimovsk Specialized Ammunition Plant, a private ammunition factory and one of the largest weapon cartridge production enterprises in the country.

“The facility is under tight security conditions, which limits our ability to oversee winter preparations,” the Moscow region’s Vice Governor Yevgeny Khromushin said last week. “We were unaware of the problem for nearly a day.”

An unidentified Moscow region official and two senior executives at the plant were arrested on suspicion of providing unsafe services, Russia’s Investigative Committee, which probes major crimes, said in a statement Tuesday.

Investigators said that Podolsk’s deputy mayor was accused of misusing authority by issuing a readiness certificate for the boiler house at the plant.

In the neighboring Tver region, the authorities opened a criminal case over the laundering of over 84 million rubles ($938,993) in heating bills paid by residents, the Astra Telegram channel reported this week, citing unidentified sources. According to investigators, the heads of the local water intake and boiler house misappropriated the heating payments for personal use.

Reacting to the heating failures, Putin on Tuesday asked Emergency Situations Minister Alexander Kurenkov to provide heat and electricity to the affected residents.

The outages appear to be the latest effect of several decades of crumbling infrastructure in Russia which have been linked to endemic corruption and mismanagement.

The overall decay of Russia's municipal infrastructure surpassed 70% in 2022, the pro-Kremlin newspaper Izvestia reported .

According to Sergei Pakhomov, head of the State Duma’s Construction, Housing and Utilities Committee, water pipes that were 90 years old or even older were still in use as recently as two years ago in some cases.

Housing, utilities and communal services are a common source of problems for Russians during the winter.

In St. Petersburg, residents regularly complain about extensive ice coverage on city streets and sidewalks, with many people ending up in the hospital over the years due to slipping and falling accidents.

In the Siberian republic of Khakassia, two villages were left without electricity last month due to apparent issues with outdated communication systems.

In the winter of 2020, five people in the Perm region were killed after a pipe burst.

When asked about the latest heating outages, Kremlin spokesman Dmitry Peskov acknowledged the problems and linked them to poor municipal infrastructure, saying that people “had to endure a lot of inconvenience in the cold and without electricity.”

"Despite all the titanic efforts to update all housing and communal services systems, there's still a certain part that remains considerably deteriorated. These programs will continue, but it is impossible to update all pipes and all housing and communal services systems in 10-15 years,” Peskov said.

As for now, residents affected by heating issues appear to lack optimism that the problems will be solved efficiently.

"It's been a week since we've had heating, and the temperature in my apartment is around 11 degrees Celsius,” Podolsk resident Lidiya told The Moscow Times.

“Unfortunately, no one knows when it will be repaired,” she added.

Turn Your Curiosity Into Discovery

Latest facts.

Tips and Tricks to Help You Create a HIPAA Compliant Email

How to Stop Facial Hair Growth in Females Naturally

40 facts about elektrostal.

Written by Lanette Mayes

Modified & Updated: 02 Mar 2024

Reviewed by Jessica Corbett

Elektrostal is a vibrant city located in the Moscow Oblast region of Russia. With a rich history, stunning architecture, and a thriving community, Elektrostal is a city that has much to offer. Whether you are a history buff, nature enthusiast, or simply curious about different cultures, Elektrostal is sure to captivate you.

This article will provide you with 40 fascinating facts about Elektrostal, giving you a better understanding of why this city is worth exploring. From its origins as an industrial hub to its modern-day charm, we will delve into the various aspects that make Elektrostal a unique and must-visit destination.

So, join us as we uncover the hidden treasures of Elektrostal and discover what makes this city a true gem in the heart of Russia.

Key Takeaways:

• Elektrostal, known as the “Motor City of Russia,” is a vibrant and growing city with a rich industrial history, offering diverse cultural experiences and a strong commitment to environmental sustainability.
• With its convenient location near Moscow, Elektrostal provides a picturesque landscape, vibrant nightlife, and a range of recreational activities, making it an ideal destination for residents and visitors alike.

Known as the “Motor City of Russia.”

Elektrostal, a city located in the Moscow Oblast region of Russia, earned the nickname “Motor City” due to its significant involvement in the automotive industry.

Home to the Elektrostal Metallurgical Plant.

Elektrostal is renowned for its metallurgical plant, which has been producing high-quality steel and alloys since its establishment in 1916.

Boasts a rich industrial heritage.

Elektrostal has a long history of industrial development, contributing to the growth and progress of the region.

Founded in 1916.

The city of Elektrostal was founded in 1916 as a result of the construction of the Elektrostal Metallurgical Plant.

Located approximately 50 kilometers east of Moscow.

Elektrostal is situated in close proximity to the Russian capital, making it easily accessible for both residents and visitors.

Known for its vibrant cultural scene.

Elektrostal is home to several cultural institutions, including museums, theaters, and art galleries that showcase the city’s rich artistic heritage.

A popular destination for nature lovers.

Surrounded by picturesque landscapes and forests, Elektrostal offers ample opportunities for outdoor activities such as hiking, camping, and birdwatching.

Hosts the annual Elektrostal City Day celebrations.

Every year, Elektrostal organizes festive events and activities to celebrate its founding, bringing together residents and visitors in a spirit of unity and joy.

Has a population of approximately 160,000 people.

Elektrostal is home to a diverse and vibrant community of around 160,000 residents, contributing to its dynamic atmosphere.

Boasts excellent education facilities.

The city is known for its well-established educational institutions, providing quality education to students of all ages.

A center for scientific research and innovation.

Elektrostal serves as an important hub for scientific research, particularly in the fields of metallurgy, materials science, and engineering.

Surrounded by picturesque lakes.

The city is blessed with numerous beautiful lakes, offering scenic views and recreational opportunities for locals and visitors alike.

Well-connected transportation system.

Elektrostal benefits from an efficient transportation network, including highways, railways, and public transportation options, ensuring convenient travel within and beyond the city.

Famous for its traditional Russian cuisine.

Food enthusiasts can indulge in authentic Russian dishes at numerous restaurants and cafes scattered throughout Elektrostal.

Home to notable architectural landmarks.

Elektrostal boasts impressive architecture, including the Church of the Transfiguration of the Lord and the Elektrostal Palace of Culture.

Offers a wide range of recreational facilities.

Residents and visitors can enjoy various recreational activities, such as sports complexes, swimming pools, and fitness centers, enhancing the overall quality of life.

Provides a high standard of healthcare.

Elektrostal is equipped with modern medical facilities, ensuring residents have access to quality healthcare services.

Home to the Elektrostal History Museum.

The Elektrostal History Museum showcases the city’s fascinating past through exhibitions and displays.

A hub for sports enthusiasts.

Elektrostal is passionate about sports, with numerous stadiums, arenas, and sports clubs offering opportunities for athletes and spectators.

Celebrates diverse cultural festivals.

Throughout the year, Elektrostal hosts a variety of cultural festivals, celebrating different ethnicities, traditions, and art forms.

Electric power played a significant role in its early development.

Elektrostal owes its name and initial growth to the establishment of electric power stations and the utilization of electricity in the industrial sector.

Boasts a thriving economy.

The city’s strong industrial base, coupled with its strategic location near Moscow, has contributed to Elektrostal’s prosperous economic status.

Houses the Elektrostal Drama Theater.

The Elektrostal Drama Theater is a cultural centerpiece, attracting theater enthusiasts from far and wide.

Popular destination for winter sports.

Elektrostal’s proximity to ski resorts and winter sport facilities makes it a favorite destination for skiing, snowboarding, and other winter activities.

Promotes environmental sustainability.

Elektrostal prioritizes environmental protection and sustainability, implementing initiatives to reduce pollution and preserve natural resources.

Home to renowned educational institutions.

Elektrostal is known for its prestigious schools and universities, offering a wide range of academic programs to students.

Committed to cultural preservation.

The city values its cultural heritage and takes active steps to preserve and promote traditional customs, crafts, and arts.

Hosts an annual International Film Festival.

The Elektrostal International Film Festival attracts filmmakers and cinema enthusiasts from around the world, showcasing a diverse range of films.

Encourages entrepreneurship and innovation.

Elektrostal supports aspiring entrepreneurs and fosters a culture of innovation, providing opportunities for startups and business development.

Offers a range of housing options.

Elektrostal provides diverse housing options, including apartments, houses, and residential complexes, catering to different lifestyles and budgets.

Home to notable sports teams.

Elektrostal is proud of its sports legacy, with several successful sports teams competing at regional and national levels.

Boasts a vibrant nightlife scene.

Residents and visitors can enjoy a lively nightlife in Elektrostal, with numerous bars, clubs, and entertainment venues.

Promotes cultural exchange and international relations.

Elektrostal actively engages in international partnerships, cultural exchanges, and diplomatic collaborations to foster global connections.

Surrounded by beautiful nature reserves.

Nearby nature reserves, such as the Barybino Forest and Luchinskoye Lake, offer opportunities for nature enthusiasts to explore and appreciate the region’s biodiversity.

Commemorates historical events.

The city pays tribute to significant historical events through memorials, monuments, and exhibitions, ensuring the preservation of collective memory.

Promotes sports and youth development.

Elektrostal invests in sports infrastructure and programs to encourage youth participation, health, and physical fitness.

Hosts annual cultural and artistic festivals.

Throughout the year, Elektrostal celebrates its cultural diversity through festivals dedicated to music, dance, art, and theater.

Provides a picturesque landscape for photography enthusiasts.

The city’s scenic beauty, architectural landmarks, and natural surroundings make it a paradise for photographers.

Connects to Moscow via a direct train line.

The convenient train connection between Elektrostal and Moscow makes commuting between the two cities effortless.

A city with a bright future.

Elektrostal continues to grow and develop, aiming to become a model city in terms of infrastructure, sustainability, and quality of life for its residents.

In conclusion, Elektrostal is a fascinating city with a rich history and a vibrant present. From its origins as a center of steel production to its modern-day status as a hub for education and industry, Elektrostal has plenty to offer both residents and visitors. With its beautiful parks, cultural attractions, and proximity to Moscow, there is no shortage of things to see and do in this dynamic city. Whether you’re interested in exploring its historical landmarks, enjoying outdoor activities, or immersing yourself in the local culture, Elektrostal has something for everyone. So, next time you find yourself in the Moscow region, don’t miss the opportunity to discover the hidden gems of Elektrostal.

Q: What is the population of Elektrostal?

A: As of the latest data, the population of Elektrostal is approximately XXXX.

Q: How far is Elektrostal from Moscow?

A: Elektrostal is located approximately XX kilometers away from Moscow.

Q: Are there any famous landmarks in Elektrostal?

A: Yes, Elektrostal is home to several notable landmarks, including XXXX and XXXX.

Q: What industries are prominent in Elektrostal?

A: Elektrostal is known for its steel production industry and is also a center for engineering and manufacturing.

Q: Are there any universities or educational institutions in Elektrostal?

A: Yes, Elektrostal is home to XXXX University and several other educational institutions.

Q: What are some popular outdoor activities in Elektrostal?

A: Elektrostal offers several outdoor activities, such as hiking, cycling, and picnicking in its beautiful parks.

Q: Is Elektrostal well-connected in terms of transportation?

A: Yes, Elektrostal has good transportation links, including trains and buses, making it easily accessible from nearby cities.

Q: Are there any annual events or festivals in Elektrostal?

A: Yes, Elektrostal hosts various events and festivals throughout the year, including XXXX and XXXX.

Was this page helpful?

Our commitment to delivering trustworthy and engaging content is at the heart of what we do. Each fact on our site is contributed by real users like you, bringing a wealth of diverse insights and information. To ensure the highest standards of accuracy and reliability, our dedicated editors meticulously review each submission. This process guarantees that the facts we share are not only fascinating but also credible. Trust in our commitment to quality and authenticity as you explore and learn with us.

Share this Fact: