Bases of the intersection cohomology of Grassmannian Schubert varieties

被引：2
|
作者：
Patimo, Leonardo [1 ]
机构：
[1] Albert Ludwigs Univ Freiburg, Freiburg, Germany
来源：
JOURNAL OF ALGEBRA | 2022年 / 589卷
基金：
美国国家科学基金会;
关键词：
Schubert varieties; Soergel bimodules; Intersection cohomology; Grassmannian; EQUIVARIANT COHOMOLOGY; KAZHDAN; LUSZTIG;
D O I：
10.1016/j.jalgebra.2021.10.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The parabolic Kazhdan-Lusztig polynomials for Grassmannians can be computed by counting Dyck partitions. We "lift" this combinatorial formula to the corresponding category of singular Soergel bimodules to obtain bases of the Horn spaces between indecomposable objects. In particular, we describe bases of intersection cohomology of Schubert varieties in Grassmannians parametrized by Dyck partitions which extend (after dualizing) the classical Schubert basis of the ordinary cohomology. (C) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页码：345 / 400
页数：56
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