"Parthasarathy-Ranga Rao-Varadarajan conjecture"의 두 판 사이의 차이
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imported>Pythagoras0 (새 문서: ==introduction== * PRV conjecture * notations ** $\nu$ integral weight ** $\overline{\nu}$ the dominant integral weight of $W\cdot \nu$ ** $V(\overline{\nu})$ highest weight represen...) |
Pythagoras0 (토론 | 기여) |
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| (다른 사용자 한 명의 중간 판 9개는 보이지 않습니다) | |||
| 2번째 줄: | 2번째 줄: | ||
* PRV conjecture | * PRV conjecture | ||
* notations | * notations | ||
| − | ** | + | ** <math>\nu</math> integral weight |
| − | ** | + | ** <math>\overline{\nu}</math> the dominant integral weight of <math>W\cdot \nu</math> |
| − | ** | + | ** <math>V(\overline{\nu})</math> highest weight representation |
| − | * | + | * <math>\lambda,\mu</math> dominant integral weights and <math>w\in W</math>, the module <math>V(\overline{\lambda+w\mu})</math> occurs with multiplicity at least one in <math>V(\lambda)\otimes V(\mu)</math> |
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| + | ==memo== | ||
| + | * http://mathoverflow.net/questions/163217/tensor-products-of-two-irreducible-representations-of-reductive-groups-and-their/163239#163239 | ||
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| + | ==related items== | ||
| + | * [[Tensor product decompositions of representations of Lie algebras]] | ||
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| + | ==expositions== | ||
| + | * Khare, Apoorva. 2012. “Representations of Complex Semi-simple Lie Groups and Lie Algebras.” arXiv:1208.0416 (August 2). http://arxiv.org/abs/1208.0416. | ||
| + | * Kumar, Shrawan. 2010. “Tensor Product Decomposition.” In Proceedings of the International Congress of Mathematicians. Volume III, 1226–1261. New Delhi: Hindustan Book Agency. http://www.ams.org/mathscinet-getitem?mr=2827839. http://www.unc.edu/math/Faculty/kumar/papers/kumar60.pdf | ||
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==articles== | ==articles== | ||
| + | * Montagard, P. L., B. Pasquier, and N. Ressayre. ‘Two Generalizations of the PRV Conjecture’. Compositio Mathematica 147, no. 04 (July 2011): 1321–36. doi:10.1112/S0010437X10005233. | ||
| + | * Kumar, Shrawan. ‘A Refinement of the PRV Conjecture’. Inventiones Mathematicae 97, no. 2 (1 June 1989): 305–11. doi:10.1007/BF01389044. | ||
* Kumar, Shrawan. 1988. “Proof of the Parthasarathy-Ranga Rao-Varadarajan Conjecture.” Inventiones Mathematicae 93 (1): 117–130. doi:10.1007/BF01393689. http://link.springer.com/article/10.1007%2FBF01393689 | * Kumar, Shrawan. 1988. “Proof of the Parthasarathy-Ranga Rao-Varadarajan Conjecture.” Inventiones Mathematicae 93 (1): 117–130. doi:10.1007/BF01393689. http://link.springer.com/article/10.1007%2FBF01393689 | ||
| + | * Parthasarathy, K. R., R. Ranga Rao, and V. S. Varadarajan. ‘Representations of Complex Semi-Simple Lie Groups and Lie Algebras’. Annals of Mathematics, Second Series, 85, no. 3 (1 May 1967): 383–429. doi:10.2307/1970351. | ||
| + | * Parthasarathy, K. R., R. Ranga Rao, and V. S. Varadarajan. ‘Representations of Complex Semisimple Lie Groups and Lie Algebras’. Bulletin of the American Mathematical Society 72, no. 3 (1966): 522–25. doi:10.1090/S0002-9904-1966-11528-8. | ||
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| + | [[분류:Lie theory]] | ||
| + | [[분류:migrate]] | ||
2020년 11월 16일 (월) 05:34 기준 최신판
introduction
- PRV conjecture
- notations
- \(\nu\) integral weight
- \(\overline{\nu}\) the dominant integral weight of \(W\cdot \nu\)
- \(V(\overline{\nu})\) highest weight representation
- \(\lambda,\mu\) dominant integral weights and \(w\in W\), the module \(V(\overline{\lambda+w\mu})\) occurs with multiplicity at least one in \(V(\lambda)\otimes V(\mu)\)
memo
expositions
- Khare, Apoorva. 2012. “Representations of Complex Semi-simple Lie Groups and Lie Algebras.” arXiv:1208.0416 (August 2). http://arxiv.org/abs/1208.0416.
- Kumar, Shrawan. 2010. “Tensor Product Decomposition.” In Proceedings of the International Congress of Mathematicians. Volume III, 1226–1261. New Delhi: Hindustan Book Agency. http://www.ams.org/mathscinet-getitem?mr=2827839. http://www.unc.edu/math/Faculty/kumar/papers/kumar60.pdf
articles
- Montagard, P. L., B. Pasquier, and N. Ressayre. ‘Two Generalizations of the PRV Conjecture’. Compositio Mathematica 147, no. 04 (July 2011): 1321–36. doi:10.1112/S0010437X10005233.
- Kumar, Shrawan. ‘A Refinement of the PRV Conjecture’. Inventiones Mathematicae 97, no. 2 (1 June 1989): 305–11. doi:10.1007/BF01389044.
- Kumar, Shrawan. 1988. “Proof of the Parthasarathy-Ranga Rao-Varadarajan Conjecture.” Inventiones Mathematicae 93 (1): 117–130. doi:10.1007/BF01393689. http://link.springer.com/article/10.1007%2FBF01393689
- Parthasarathy, K. R., R. Ranga Rao, and V. S. Varadarajan. ‘Representations of Complex Semi-Simple Lie Groups and Lie Algebras’. Annals of Mathematics, Second Series, 85, no. 3 (1 May 1967): 383–429. doi:10.2307/1970351.
- Parthasarathy, K. R., R. Ranga Rao, and V. S. Varadarajan. ‘Representations of Complex Semisimple Lie Groups and Lie Algebras’. Bulletin of the American Mathematical Society 72, no. 3 (1966): 522–25. doi:10.1090/S0002-9904-1966-11528-8.