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

Alfréd Rényi Institute of Mathematics

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

1 Scopus citations

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

Bibliographical note

Publisher Copyright:
© 2021 The Author(s)

Funding

PH was partially supported by Hungarian National Research, Development and Innovation Office ( NKFIH ), Grant No. K115799 , and by a visiting grant from Bar-Ilan University . The project leading to this application has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, Grant agreement No. 741420 . RMA and YR were partially supported by the Israel Science Foundation , Grant No. 1970/18 .

Funders	Funder number
Horizon 2020 Framework Programme
European Commission
Israel Science Foundation	1970/18
Horizon 2020	741420
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal	K115799

Keywords

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

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10.1016/j.jalgebra.2021.10.034

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AU - Hegedüs, Pál

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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.

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KW - Arc permutation

KW - Factorisation of the Coxeter element

KW - Flip

KW - Gelfand subgroup

KW - Group action

KW - Triangulation

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ER -

Combinatorial flip actions and Gelfand pairs for affine Weyl groups

Abstract

Bibliographical note

Funding

Keywords

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