A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs

Omar Tout*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

After a careful consideration of some of the well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs, we were able to deduce a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coefficients of its associated double-class algebra can be written in terms of zonal spherical functions. This is a generalization of the Frobenius formula which expresses the structure coefficients of the center of a finite group algebra in terms of irreducible characters.

Original languageEnglish
Pages (from-to)4944-4959
Number of pages16
JournalCommunications in Algebra
Volume45
Issue number11
DOIs
Publication statusPublished - Nov 2 2017
Externally publishedYes

Keywords

  • Double-class algebras
  • Gelfand pairs and zonal spherical functions
  • group algebras
  • representation theory of finite groups
  • structure coefficients

ASJC Scopus subject areas

  • Algebra and Number Theory

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