"Gelfand-Tsetlin bases"의 두 판 사이의 차이

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http://arxiv.org/abs/math/0211289
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==introduction==
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* In the fifties Gelfand posed the question of how to find a good basis for irreducible representations of reductive groups. In a paper with Zeitlin he defined special bases for irreducible representations of the general linear group and orthogonal groups.
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* <math>L(\lambda)</math> : finite-dimensional irreducible representation of <math>\mathfrak{gl}_n</math> with the highest weight <math>\lambda=(\lambda_1\geq \lambda_2\geq \cdots\geq\lambda_n\geq 0)</math> of weakly decreasing non-negative integer sequence
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* the set of all Gelfand-Zetlin patterns form a basis of <math>L(\lambda)</math>
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==identity==
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* LHS is the Weyl dimension formula for a representation of <math>\mathfrak{gl}_n</math>, and RHS is the number of elements in Gelfand-Zetlin basis
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* http://math.stackexchange.com/questions/1660/direct-proof-of-gelfand-zetlin-identity
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==related items==
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* [[Brauer-Weyl-Frobenius-Schur theory]]
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* [[Crystal bases]]
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==computational resource==
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* https://docs.google.com/file/d/0B8XXo8Tve1cxZ1AzOXgwQ0FXX1E/edit
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==encyclopedia==
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* http://en.wikipedia.org/wiki/Gelfand%E2%80%93Zeitlin_integrable_system
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==expositions==
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* Molev, A. I. 2002. “Gelfand-Tsetlin Bases for Classical Lie Algebras”. ArXiv e-print math/0211289. http://arxiv.org/abs/math/0211289.
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==articles==
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* Igor Makhlin, Weyl's Formula as the Brion Theorem for Gelfand-Tsetlin Polytopes, arXiv:1409.7996 [math.RT], September 29 2014, http://arxiv.org/abs/1409.7996
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* Gornitskii, A. A. “Essential Signatures and Canonical Bases for Irreducible Representations of <math>D_4</math>.” arXiv:1507.07498 [math], July 27, 2015. http://arxiv.org/abs/1507.07498.
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* Futorny, Vyacheslav, Dimitar Grantcharov, and Luis Enrique Ramirez. “Generic Irreducible Gelfand-Tsetlin Modules of Gl(n).” arXiv:1409.8413 [math], September 30, 2014. http://arxiv.org/abs/1409.8413.
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* Makhlin, Igor. “Weyl’s Formula as the Brion Theorem for Gelfand-Tsetlin Polytopes.” arXiv:1409.7996 [math], September 29, 2014. http://arxiv.org/abs/1409.7996.
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* Futorny, Vyacheslav, Dimitar Grantcharov, and Luis Enrique Ramirez. “Singular Gelfand-Tsetlin Modules of <math>\mathfrak{gl}(n)</math>.” arXiv:1409.0550 [math], September 1, 2014. http://arxiv.org/abs/1409.0550.
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* Hersh, Patricia, and Cristian Lenart. 2010. “Combinatorial Constructions of Weight Bases: The Gelfand-Tsetlin Basis.” Electronic Journal of Combinatorics 17 (1): Research Paper 33, 14. http://www.albany.edu/~lenart/articles/gt-basis1.pdf
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* Refaghat, H., and M. Shahryari. 2010. “A Formula for the Number of Gelfand-Zetlin Patterns.” Journal of Generalized Lie Theory and Applications 4: Art. ID G100201, 8. doi:10.4303/jglta/G100201. http://www.ashdin.com/journals/jglta/2010/G100201.pdf
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* Gel'fand, I. M., and M. L. Cetlin. 1950. “Finite-dimensional Representations of the Group of Unimodular Matrices.” Doklady Akad. Nauk SSSR (N.S.) 71: 825–828.
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[[분류:math and physics]]
 
[[분류:math and physics]]
 
[[분류:Lie theory]]
 
[[분류:Lie theory]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q5530430 Q5530430]
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===Spacy 패턴 목록===
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* [{'LOWER': 'gelfand'}, {'OP': '*'}, {'LOWER': 'zeitlin'}, {'LOWER': 'integrable'}, {'LEMMA': 'system'}]

2021년 2월 17일 (수) 03:03 기준 최신판

introduction

  • In the fifties Gelfand posed the question of how to find a good basis for irreducible representations of reductive groups. In a paper with Zeitlin he defined special bases for irreducible representations of the general linear group and orthogonal groups.
  • \(L(\lambda)\) : finite-dimensional irreducible representation of \(\mathfrak{gl}_n\) with the highest weight \(\lambda=(\lambda_1\geq \lambda_2\geq \cdots\geq\lambda_n\geq 0)\) of weakly decreasing non-negative integer sequence
  • the set of all Gelfand-Zetlin patterns form a basis of \(L(\lambda)\)


identity


related items


computational resource


encyclopedia


expositions


articles

  • Igor Makhlin, Weyl's Formula as the Brion Theorem for Gelfand-Tsetlin Polytopes, arXiv:1409.7996 [math.RT], September 29 2014, http://arxiv.org/abs/1409.7996
  • Gornitskii, A. A. “Essential Signatures and Canonical Bases for Irreducible Representations of \(D_4\).” arXiv:1507.07498 [math], July 27, 2015. http://arxiv.org/abs/1507.07498.
  • Futorny, Vyacheslav, Dimitar Grantcharov, and Luis Enrique Ramirez. “Generic Irreducible Gelfand-Tsetlin Modules of Gl(n).” arXiv:1409.8413 [math], September 30, 2014. http://arxiv.org/abs/1409.8413.
  • Makhlin, Igor. “Weyl’s Formula as the Brion Theorem for Gelfand-Tsetlin Polytopes.” arXiv:1409.7996 [math], September 29, 2014. http://arxiv.org/abs/1409.7996.
  • Futorny, Vyacheslav, Dimitar Grantcharov, and Luis Enrique Ramirez. “Singular Gelfand-Tsetlin Modules of \(\mathfrak{gl}(n)\).” arXiv:1409.0550 [math], September 1, 2014. http://arxiv.org/abs/1409.0550.
  • Hersh, Patricia, and Cristian Lenart. 2010. “Combinatorial Constructions of Weight Bases: The Gelfand-Tsetlin Basis.” Electronic Journal of Combinatorics 17 (1): Research Paper 33, 14. http://www.albany.edu/~lenart/articles/gt-basis1.pdf
  • Refaghat, H., and M. Shahryari. 2010. “A Formula for the Number of Gelfand-Zetlin Patterns.” Journal of Generalized Lie Theory and Applications 4: Art. ID G100201, 8. doi:10.4303/jglta/G100201. http://www.ashdin.com/journals/jglta/2010/G100201.pdf
  • Gel'fand, I. M., and M. L. Cetlin. 1950. “Finite-dimensional Representations of the Group of Unimodular Matrices.” Doklady Akad. Nauk SSSR (N.S.) 71: 825–828.

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'gelfand'}, {'OP': '*'}, {'LOWER': 'zeitlin'}, {'LOWER': 'integrable'}, {'LEMMA': 'system'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Gelfand-Tsetlin_bases&oldid=51890"