共不变II的$\hat{sl_2}$空间的组合学
Combinatorics of the $\hat{sl_2}$ spaces of coinvariants II
摘要：
共不变量空间是可积$\hat{sl_2}$模通过由复直线上的一组点标记的某些子代数的作用生成的子空间的商空间。当所有的点都不同时，共不变空间与WZW共形域论中的共形块空间基本一致，它们的维数由Verlinde规则给出.本文描述了共不变的$\wsl$空间的单项基，特别地，我们证明了当所有点重合时，共不变的空间具有相同的维数.建立了单项基所满足的递归关系和共不变空间的相应特征。为了证明，我们使用了$\hat{\mathfrak{sl}}_2$模的滤子，以及第一个滤子在伴随分次空间上的进一步滤子。本文是[FKLMM]的继续。
英文摘要：
The spaces of coinvariants are quotient spaces of integrable $\hat{sl_2}$ modules by subspaces generated by actions of certain subalgebras labeled by a set of points on a complex line. When all the points are distinct, the spaces of coinvariants essentially coincide with the spaces of conformal blocks in the WZW conformal field theory and their dimensions are given by the Verlinde rule. We describe monomial bases for the $\wsl$ spaces of coinvariants, In particular, we prove that the spaces of coinvariants have the same dimensions when all the points coincide. We establish recursive relations satisfied by the monomial bases and the corresponding characters of the spaces of coinvariants. For the proof we use filtrations of the $\hat{\mathfrak{sl}}_2$ modules, and further filtrations on the adjoint graded spaces for the first filtrations. This paper is the continuation of [FKLMM].
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