Restriction of characters to subgroups of wreath products and basic sets for the symmetric group

Jean-Baptiste Gramain*, Adriana Marciuk

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

In this paper, we give the decomposition into irreducible characters of the restriction to the wreath product Zp−1 o Sw of any irreducible character of (Zp o Zp−1) o Sw, where p is any odd prime, w ≥ 0 is an integer, and Zp and Zp−1 denote the cyclic groups of order p and p − 1 respectively. This answers the question of how to decompose the restrictions to p-regular elements of irreducible characters of the symmetric group Sn in the Z-basis corresponding to the p-basic set of Sn described by Brunat and Gramain in [1]. The result is given in terms of the Littlewood-Richardson coefficients for the symmetric group.
Original languageEnglish
Pages (from-to)2428-2441
Number of pages14
JournalCommunications in Algebra
Volume48
Issue number6
Early online date30 Jan 2020
DOIs
Publication statusPublished - 2020

Keywords

  • basic sets
  • character theory
  • representation theory
  • symmetric group
  • wreath products
  • Basic sets

Fingerprint Dive into the research topics of 'Restriction of characters to subgroups of wreath products and basic sets for the symmetric group'. Together they form a unique fingerprint.

Cite this