One-skeleton posets of Bruhat interval polytopes

被引：1
|
作者：
Gaetz, Christian [1 ]
机构：
[1] Cornell Univ, Dept Math, Ithaca, NY 14850 USA
来源：
ADVANCES IN MATHEMATICS | 2023年 / 430卷
关键词：
Bruhat interval polytope; Weak order; Lattice; Schubert variety; Torus orbit; Smooth; VARIETIES;
D O I：
10.1016/j.aim.2023.109216
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Introduced by Kodama and Williams, Bruhat interval poly -topes are generalized permutohedra closely connected to the study of torus orbit closures and total positivity in Schubert varieties. We show that the 1-skeleton posets of these poly -topes are lattices and classify when the polytopes are simple, thereby resolving open problems and conjectures of Fraser, of Lee-Masuda, and of Lee-Masuda-Park. In particular, we classify when generic torus orbit closures in Schubert varieties are smooth. & COPY; 2023 Elsevier Inc. All rights reserved.
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页数：22
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