Hook flag characters and their combinatorics
type: Item
instance of: scholarly article
title: Hook flag characters and their combinatorics
zbMATH Open document ID: 0547.20010
DOI: 10.1016/0022-4049(85)90042-8
published in: Journal of Pure and Applied Algebra
publication date: 1985-01-01T00:00:00Z
review text: These are the characters \(\chi(a;b)\) of the representations of \(S_ n\) induced by the representations \([a_ 1]\#...\#[a_ k]\#[1^{b_ 1}]\#...\#[1^{b_ l}]\) of the subgroups \(S(a;b):=S_{a_ 1}\times...\times S_{a_ k}\times S_{b_ 1}\times,..\times S_{b_ l}\) (natural embedding), were \(\sum a_ i+\sum b_ j=n\). Continuing earlier research [(to appear in) Adv. Math. 64, 118--175 (1987; Zbl 0617.17002)] the authors decompose \(\chi(a;b)\otimes\chi(c;d)\) and give a construction analogous to the Schensted-Knuth correspondence adapted to so-called \((k,l)\)-semistandard tableaux which are needed here.
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 3871621
zbMATH Keywords: symmetric groups
zbMATH Keywords: hook representations
zbMATH Keywords: characters
zbMATH Keywords: Schensted-Knuth correspondence
zbMATH Keywords: semistandard tableaux
author: Allan Berele
author: Jeffrey Remmel
reviewed by: Adalbert Kerber
MaRDI profile type: Publication
full work available at URL: 0022-4049(85)90042-8
OpenAlex ID: W2092027924
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description: scientific article; zbMATH DE number 3871621