"Tilting modules for quantum groups"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
| − | * modules for | + | * modules for <math>U_q(\mathfrak{g})</math> |
| − | * [[Verma modules]] | + | * [[Verma modules]] <math>M_{\lambda}=U_q(\mathfrak{g})\otimes_{U_q(\mathfrak{b})}\mathbb{C}_{\lambda}</math> |
* Weyl modules : quotients of Verma modules | * Weyl modules : quotients of Verma modules | ||
| − | + | :<math> | |
| − | W_{\lambda}=M_{\lambda}/\ | + | W_{\lambda}=M_{\lambda}/\operatorname{span}(M_{s_i\cdot \lambda}) |
| − | + | </math> | |
| − | * a tilting module is a module | + | * a tilting module is a module <math>T</math> that admits a filtration whose associated graded pieces are Weyl modules and that admits another filtration whose associated graded are dual Weyl modules |
| + | |||
| + | |||
| + | ==expositions== | ||
| + | * http://sms.cam.ac.uk/media/642709 | ||
| + | |||
| + | |||
| + | ==articles== | ||
| + | * Hazi, Amit. “Balanced Semisimple Filtrations for Tilting Modules.” arXiv:1510.02596 [math], October 9, 2015. http://arxiv.org/abs/1510.02596. | ||
| + | * Andersen, Henning Haahr, Catharina Stroppel, and Daniel Tubbenhauer. “Cellular Structures Using <math>\textbf{U}_q</math>-Tilting Modules.” arXiv:1503.00224 [math], March 1, 2015. http://arxiv.org/abs/1503.00224. | ||
| + | * Andersen, Henning Haahr, and Masaharu Kaneda. 2009. “Rigidity of Tilting Modules.” arXiv:0909.2935 [math] (September 16). http://arxiv.org/abs/0909.2935. | ||
| + | * Andersen, Henning Haahr, and Jan Paradowski. 1995. “Fusion Categories Arising from Semisimple Lie Algebras.” Communications in Mathematical Physics 169 (3) (May 1): 563–588. doi:[http://dx.doi.org/10.1007/BF02099312 10.1007/BF02099312]. | ||
| + | [[분류:migrate]] | ||
2020년 11월 16일 (월) 04:27 기준 최신판
introduction
- modules for \(U_q(\mathfrak{g})\)
- Verma modules \(M_{\lambda}=U_q(\mathfrak{g})\otimes_{U_q(\mathfrak{b})}\mathbb{C}_{\lambda}\)
- Weyl modules : quotients of Verma modules
\[ W_{\lambda}=M_{\lambda}/\operatorname{span}(M_{s_i\cdot \lambda}) \]
- a tilting module is a module \(T\) that admits a filtration whose associated graded pieces are Weyl modules and that admits another filtration whose associated graded are dual Weyl modules
expositions
articles
- Hazi, Amit. “Balanced Semisimple Filtrations for Tilting Modules.” arXiv:1510.02596 [math], October 9, 2015. http://arxiv.org/abs/1510.02596.
- Andersen, Henning Haahr, Catharina Stroppel, and Daniel Tubbenhauer. “Cellular Structures Using \(\textbf{U}_q\)-Tilting Modules.” arXiv:1503.00224 [math], March 1, 2015. http://arxiv.org/abs/1503.00224.
- Andersen, Henning Haahr, and Masaharu Kaneda. 2009. “Rigidity of Tilting Modules.” arXiv:0909.2935 [math] (September 16). http://arxiv.org/abs/0909.2935.
- Andersen, Henning Haahr, and Jan Paradowski. 1995. “Fusion Categories Arising from Semisimple Lie Algebras.” Communications in Mathematical Physics 169 (3) (May 1): 563–588. doi:10.1007/BF02099312.