"Tilting modules for quantum groups"의 두 판 사이의 차이
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imported>Pythagoras0 (새 문서: ==introduction== * Verma modules * Weyl modules : quotients of Verma modules) |
imported>Pythagoras0 |
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==introduction== | ==introduction== | ||
| − | * Verma modules | + | * 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 | * Weyl modules : quotients of Verma modules | ||
| + | $$ | ||
| + | W_{\lambda}=M_{\lambda}/\rm{span}(M_{s_i\cdot \lambda}) | ||
| + | $$ | ||
| + | * a tilting module is a module $T$ that admies a filtration whose associated graded pieces are Weyl modules | ||
2013년 6월 26일 (수) 02:17 판
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
$$ W_{\lambda}=M_{\lambda}/\rm{span}(M_{s_i\cdot \lambda}) $$
- a tilting module is a module $T$ that admies a filtration whose associated graded pieces are Weyl modules