Sheaves on moment graphs and a localization of Verma flags
Sheaves on moment graphs and a localization of Verma flags
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力矩图上的滑轮和 Verma 标志的本地化
DOI：
10.1016/j.aim.2007.08.008
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发表时间：
2005
影响因子：
1.7
通讯作者：
P. Fiebig
中科院分区：
文献类型：
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作者：
P. Fiebig
对于任意矩图G，我们赋予G上层范畴的一个子范畴V和一个精确结构。我们表明，在这种情况下，该图是相关联的一个非临界块的等变范畴O的对称化的Kac-穆迪代数，V是等价的（作为一个确切的类别）的子范畴的模块，承认一个Verma标志。投射模在这个等价下对应于图上的交上同调层，因此，根据布雷登和麦克弗森的定理，对应于与卡茨-穆迪群相关联的舒伯特簇的等变交上同调。
To any moment graph G we assign a subcategory V of the category of sheaves on G together with an exact structure. We show that in the case that the graph is associated to a non-critical block of the equivariant category O over a symmetrizable Kac–Moody algebra, V is equivalent (as an exact category) to the subcategory of modules that admit a Verma flag. The projective modules correspond under this equivalence to the intersection cohomology sheaves on the graph, and hence, by a theorem of Braden and MacPherson, to the equivariant intersection cohomologies of Schubert varieties associated to Kac–Moody groups.