"Gelfand-Tsetlin bases"의 두 판 사이의 차이
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==introduction== | ==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. | * 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. | ||
| − | * | + | * <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 |
| − | * the set of all Gelfand-Zetlin patterns form a basis of | + | * the set of all Gelfand-Zetlin patterns form a basis of <math>L(\lambda)</math> |
==identity== | ==identity== | ||
| − | * LHS is the Weyl dimension formula for a representation of | + | * 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 |
* http://math.stackexchange.com/questions/1660/direct-proof-of-gelfand-zetlin-identity | * http://math.stackexchange.com/questions/1660/direct-proof-of-gelfand-zetlin-identity | ||
| 30번째 줄: | 30번째 줄: | ||
==articles== | ==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 | * 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 | + | * 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. |
* 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. | * 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. | * 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 | + | * 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. |
* 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 | * 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 | * 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 | ||
| 42번째 줄: | 42번째 줄: | ||
[[분류:Lie theory]] | [[분류:Lie theory]] | ||
[[분류:migrate]] | [[분류:migrate]] | ||
| + | |||
| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q5530430 Q5530430] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'gelfand'}, {'OP': '*'}, {'LOWER': 'zeitlin'}, {'LOWER': 'integrable'}, {'LEMMA': 'system'}] | ||
2021년 2월 17일 (수) 02:03 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
- LHS is the Weyl dimension formula for a representation of \(\mathfrak{gl}_n\), and RHS is the number of elements in Gelfand-Zetlin basis
- http://math.stackexchange.com/questions/1660/direct-proof-of-gelfand-zetlin-identity
computational resource
encyclopedia
expositions
- Molev, A. I. 2002. “Gelfand-Tsetlin Bases for Classical Lie Algebras”. ArXiv e-print math/0211289. http://arxiv.org/abs/math/0211289.
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
- ID : Q5530430
Spacy 패턴 목록
- [{'LOWER': 'gelfand'}, {'OP': '*'}, {'LOWER': 'zeitlin'}, {'LOWER': 'integrable'}, {'LEMMA': 'system'}]