Combinatorial flip actions and Gelfand pairs for affine Weyl groups

Ron M. Adin, Pál Hegedüs, Yuval Roichman

Research output: Contribution to journalArticlepeer-review


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
Early online date15 Nov 2021
StatePublished - 1 Oct 2022


  • 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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