Tilting modules for quantum groups
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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.