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

Omar Tout

doi:10.1142/S0219498821500857

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

Omar Tout^*

^*Corresponding author for this work

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

1 Citation (Scopus)

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 language	English
Article number	2150085
Journal	Journal of Algebra and Its Applications
Volume	20
Issue number	5
DOIs	https://doi.org/10.1142/S0219498821500857
Publication status	Published - May 2021
Externally published	Yes

Keywords

Hyperoctahedral group
Symmetric Gelfand pairs

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

Access to Document

10.1142/S0219498821500857

Cite this

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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.",

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