"Representations of symmetrizable Kac-Moody algebras"의 두 판 사이의 차이

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-==introduction==
-* Let $L(A)$ be a symmetrizable Kac-Moody algebra
-* the category <math>\mathcal{O}</math>
-* Integrable modules
-==the category $\mathcal{O}$==
-* $V$ is an object in $\mathcal{O}$
-# $V=\oplus_{\lambda\in \mathfrak{h}^{*}}V_{\lambda}$
-# $\dim V_{\lambda}$ is finite for each $\lambda\in \mathfrak{h}^{*}$
-# there exists a finite set $\lambda_1,\cdots, \lambda_s\in \mathfrak{h}^{*}$ such that each $\lambda$ with $V_{\lambda}\neq 0$ satisfies $\lambda \prec \lambda_i$ for some $i\in \{1,\cdots, s\}$
-==integrable module==
-* An $L(A)$-module $V$ is called integrable if
-$$
-V=\oplus_{\lambda\in \mathfrak{h}^{*}}V_{\lambda}
-$$
-and if $e_i : V\to V$ and $f_i : V\to V$ are locally nilpotent for all $i$
-;Thm
-Let $L(A)$ be a symmetrizable Kac-Moody algebra and $L(\lambda)$ be an irreducible $L(A)$-module in the category $\mathcal{O}$. Then $L(\lambda)$ is integrable if and only if $\lambda$ is dominant and integral.
-* [[Weyl-Kac character formula]]
-==related items==
-* [[BGG category and BGG resolution]]
-[[분류:Lie theory]]

2020년 11월 13일 (금) 20:56 판