On the symmetric Gelfand pair (ℋn× ℋn-1, diag (ℋn-1))

Omar Tout*

*Corresponding author for this work

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Abstract

We show that the ℋn-1-conjugacy classes of ℋn, where ℋn is the hyperoctahedral group on 2n elements, are indexed by marked bipartitions of n. This will lead us to prove that (ℋn ×ℋn-1,diag(ℋn-1)) is a symmetric Gelfand pair and that the induced representation 1diag(ℋn-1)ℋn×ℋn-1 is multiplicity free.

Original languageEnglish
Article number2150085
JournalJournal of Algebra and Its Applications
Volume20
Issue number5
DOIs
Publication statusPublished - May 2021
Externally publishedYes

Keywords

  • Hyperoctahedral group
  • Symmetric Gelfand pairs

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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