A combinatorial study of affine Schubert varieties in affine Grassmannian
A combinatorial study of affine Schubert varieties in affine Grassmannian
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仿射格拉斯曼中仿射舒伯特簇的组合研究
DOI：
10.1007/s00031-020-09634-9
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发表时间：
2021
影响因子：
0.7
通讯作者：
Hong, Jiuzu
中科院分区：
文献类型：
--
作者：
Besson, Marc;Hong, Jiuzu
设为伴随型单代数群G的仿射Grassmanian Gr中I-轨道的闭包，其中I是Iwahori子群，λ是G的余权。我们找到了一个简单的算法，它用余权来描述所有I-轨道的集合λ（λ）。在G的余权格上引入了R-算子（与正根相关），它精确地刻画了I-轨道的闭包关系.这些算子一般在余权格上满足Braid关系。我们还建立了一个集λ（λ）与一级仿射Demazure模的权系之间的对偶 用λ表示，其中是与G的李代数相关联的仿射Kac-Moody李代数对偶的仿射Kac-Moody代数。
Letbe the closure of the I-orbitin the affine Grassmanian Gr of a simple algebraic groupGof adjoint type, where I is the Iwahori subgroup and λ is a coweight ofG. We find a simple algorithm which describes the set Ψ(λ) of all I-orbits inin terms of coweights. We introduceR-operators (associated to positive roots) on the coweight lattice ofG, which exactly describe the closure relation of I-orbits. These operators satisfy Braid relations generically on the coweight lattice. We also establish a duality between the set Ψ(λ) and the weight system of the level one affine Demazure module ofindexed by λ, whereis the affine Kac–Moody algebra dual to the affine Kac–Moody Lie algebraassociated to the Lie algebraofG.