Combinatorial flip actions and Gelfand pairs for affine Weyl groups

Ron M. Adin; Pál Hegedüs; Yuval Roichman

doi:10.1016/j.jalgebra.2021.10.034

Combinatorial flip actions and Gelfand pairs for affine Weyl groups

Ron M. Adin, Pál Hegedüs, Yuval Roichman

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

Several combinatorial actions of the affine Weyl group of type C˜_n on triangulations, trees, words and permutations are compared. Addressing a question of David Vogan, we show that, modulo a natural involution, these permutation representations are multiplicity-free. The proof uses a general construction of Gelfand subgroups in the affine Weyl groups of types C˜_n and B˜_n.

Original language	English
Pages (from-to)	5-33
Number of pages	29
Journal	Journal of Algebra
Volume	607
Early online date	15 Nov 2021
DOIs	https://doi.org/10.1016/j.jalgebra.2021.10.034
State	Published - 1 Oct 2022

Keywords

Affine Weyl group
Arc permutation
Factorisation of the Coxeter element
Flip
Gelfand subgroup
Group action
Triangulation

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2021.10.034

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title = "Combinatorial flip actions and Gelfand pairs for affine Weyl groups",

abstract = "Several combinatorial actions of the affine Weyl group of type C˜n on triangulations, trees, words and permutations are compared. Addressing a question of David Vogan, we show that, modulo a natural involution, these permutation representations are multiplicity-free. The proof uses a general construction of Gelfand subgroups in the affine Weyl groups of types C˜n and B˜n.",

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doi = "10.1016/j.jalgebra.2021.10.034",

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T1 - Combinatorial flip actions and Gelfand pairs for affine Weyl groups

AU - Adin, Ron M.

AU - Hegedüs, Pál

AU - Roichman, Yuval

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Y1 - 2022/10/1

N2 - Several combinatorial actions of the affine Weyl group of type C˜n on triangulations, trees, words and permutations are compared. Addressing a question of David Vogan, we show that, modulo a natural involution, these permutation representations are multiplicity-free. The proof uses a general construction of Gelfand subgroups in the affine Weyl groups of types C˜n and B˜n.

AB - Several combinatorial actions of the affine Weyl group of type C˜n on triangulations, trees, words and permutations are compared. Addressing a question of David Vogan, we show that, modulo a natural involution, these permutation representations are multiplicity-free. The proof uses a general construction of Gelfand subgroups in the affine Weyl groups of types C˜n and B˜n.

KW - Affine Weyl group

KW - Arc permutation

KW - Factorisation of the Coxeter element

KW - Flip

KW - Gelfand subgroup

KW - Group action

KW - Triangulation

UR - http://www.scopus.com/inward/record.url?scp=85120162980&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2021.10.034

DO - 10.1016/j.jalgebra.2021.10.034

M3 - مقالة

SN - 0021-8693

VL - 607

SP - 5

EP - 33

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Combinatorial flip actions and Gelfand pairs for affine Weyl groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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