Appendix to Syu Kato and Sergey Loktev: A Weyl module stratification of integrable representations
Appendix to Syu Kato and Sergey Loktev: A Weyl module stratification of integrable representations
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Syu Kato 和 Sergey Loktev 的附录：可积表示的 Weyl 模块分层
DOI：
10.1007/s00220-019-03327-5
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发表时间：
2019
影响因子：
2.4
通讯作者：
Ryosuke Kodera
中科院分区：
文献类型：
--
作者：
Ryosuke Kodera
我们在仿射李代数的可积最高权模上构造了一个滤子，该李代数的伴随分次商是全局Weyl模的直和。我们证明了每个整体Weyl模的分次重数由相应的水平限制Kostka多项式给出。这导致了一个解释的水平限制Kostka多项式的分次维数的空间的共形coinvariants。此外，作为主要结果的第一级情形的应用，我们实现了Boris Feigin所预言的厚仿射Grassmanian的Schubert子簇形式的当前代数的全局Weyl模。
We construct a filtration on an integrable highest weight module of an affine Lie algebra whose adjoint graded quotient is a direct sum of global Weyl modules. We show that the graded multiplicity of each global Weyl module there is given by the corresponding level-restricted Kostka polynomial. This leads to an interpretation of level-restricted Kostka polynomials as the graded dimension of the space of conformal coinvariants. In addition, as an application of the level one case of the main result, we realize global Weyl modules of current algebras of typein terms of Schubert subvarieties of thick affine Grassmanian, as predicted by Boris Feigin.