Combinatorial flip actions and Gelfand pairs for affine Weyl groups

Ron M. Adin, Pál Hegedüs, Yuval Roichman

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)5-33
Number of pages29
JournalJournal of Algebra
Volume607
Early online date15 Nov 2021
DOIs
StatePublished - 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 .

FundersFunder number
Horizon 2020 Framework Programme
European Research Council
Israel Science Foundation1970/18
Horizon 2020741420
Nemzeti Kutatási Fejlesztési és Innovációs HivatalK115799

    Keywords

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

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