A general framework for the polynomiality property of the structure coefficients of double-class algebras

Omar Tout*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we build a general framework in which we give a formula that shows the form of the structure coefficients of double-class algebras and centers of group algebras. This formula allows us to give a polynomiality property for the structure coefficients of some important algebras. In particular, we re-obtain the polynomiality property of the structure coefficients in the cases of the center of the symmetric group algebra and the Hecke algebra of the pair (S2 n, Bn). We also assign a new polynomiality property for the structure coefficients of the center of the hyperoctahedral group algebra and the Hecke algebra of the pair (Sn×Sn-1opp,diag(Sn-1)).

Original languageEnglish
Pages (from-to)1111-1152
Number of pages42
JournalJournal of Algebraic Combinatorics
Volume45
Issue number4
DOIs
Publication statusPublished - Jun 1 2017
Externally publishedYes

Keywords

  • Center of the hyperoctahedral group algebra
  • Centers of group algebras
  • Double-class algebras
  • Hecke algebra of the pair(S × S , diag(S))
  • Polynomiality property of the structure coefficients
  • Structure coefficients

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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