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Lee, Eun Jeong
기하학 수리물리 연구단
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Toric Bruhat interval polytopes

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Title
Toric Bruhat interval polytopes
Author(s)
Eunjeong Lee; Masuda, Mikiya; Park, Seonjeong
Publication Date
2021-04
Journal
JOURNAL OF COMBINATORIAL THEORY SERIES A, v.179
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
For two elements v and w of the symmetric group S-n with v <= w in Bruhat order, the Bruhat interval polytope Q(v,w) is the convex hull of the points (z(1), ..., z(n)) is an element of R-n with v <= z <= w. It is known that the Bruhat interval polytope Q(v,w) is the moment map image of the Richardson variety X-w-1(v-1). We say that Q(v,w) is toricif the corresponding Richardson variety X-w-1(v-1) is a toric variety. We show that when Q(v,w) is toric, its combinatorial type is determined by the poset structure of the Bruhat interval [v, w] while this is not true unless Q(v,w) is toric. We are concerned with the problem of when Q(v,w) is (combinatorially equivalent to) a cube because Q(v,w) is a cube if and only if X-w-1(v-1) is a smooth toric variety. We show that a Bruhat interval polytope Q(v,w) is a cube if and only if Q(v,w) is toric and the Bruhat interval [v, w] is a Boolean algebra. We also give several sufficient conditions on vand wfor Q(v,w) to be a cube. (C) 2020 Elsevier Inc. All rights reserved.
URI
https://pr.ibs.re.kr/handle/8788114/9274
DOI
10.1016/j.jcta.2020.105387
ISSN
0097-3165
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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