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Lee, Eun Jeong
기하학 수리물리 연구단
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Torus orbit closures in flag varieties and retractions on Weyl groups

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Title
Torus orbit closures in flag varieties and retractions on Weyl groups
Author(s)
Eunjeong Lee; Masuda, Mikiya; Park, Seonjeong
Publication Date
2022-03
Journal
International Journal of Mathematics, v.33, no.4
Publisher
World Scientific
Abstract
A finite Coxeter group W has a natural metric d and if M is a subset of W, then for each u ∈ W, there is q ∈ M such that d(u,q) = d(u,M). Such q is not unique in general but if M is a Coxeter matroid, then it is unique, and we define a retraction Rm: W → M ⊂ W so that Rm(u) = q. The T-fixed point set YT of a T-orbit closure Y in a flag variety G/B is a Coxeter matroid, where G is a semi-simple algebraic group, B is a Borel subgroup, and T is a maximal torus of G contained in B. We define a retraction RYg: W → YT W geometrically, where W is the Weyl group of G, and show that RYg = R YTm. We introduce another retraction Ra: W → W algebraically for an arbitrary subset M of W when W is a Weyl group of classical Lie type, and show that Ra = Rm when M is a Coxeter matroid.
URI
https://pr.ibs.re.kr/handle/8788114/12214
DOI
10.1142/S0129167X22500288
ISSN
0129-167X
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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