\(p\)-restriction of partitions and homomorphisms between Specht modules.
type: Item
instance of: scholarly article
title: \(p\)-restriction of partitions and homomorphisms between Specht modules.
zbMATH Open document ID: 1107.20010
author: Matthew Fayers
author: Sinéad Lyle
author: S. Martin
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
review text: Let \(\lambda\) be a partition of \(n\) and \(\mathbb{S}_n\) be the symmetric group on \(n\) letters. Let \(F\) be a field of characteristic \(p\). Let \(S^\lambda\) denote a Specht module for the group algebra \(F\mathbb{S}_n\). An interesting problem concerning Specht modules is the determination of the homomorphism space \(\Hom_{F\mathbb{S}_n}(S^\lambda,S^\mu)\) for partitions \(\lambda\) and \(\mu\) of \(\mathbb{S}_n\). The authors, using elementary methods of Young tableaux, prove that \(\Hom_{F\mathbb{S}_n}(S^\lambda,S^\mu)\) is one-dimensional whenever \(\mu\) is the \(p\)-restriction of \(\lambda\).
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 5078338
zbMATH Keywords: Specht modules
zbMATH Keywords: symmetric groups
zbMATH Keywords: characters
zbMATH Keywords: Young tableaux
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2005.11.040
OpenAlex ID: W2066546894
cites work: On homomorphisms between Weyl modules and Specht modules
cites work: Homomorphisms between Specht modules.
cites work: On the decomposition matrices of the symmetric groups. II
cites work: Q3952291
cites work: The representation theory of the symmetric groups
cites work: Homomorphisms between neighbouring Weyl modules
DOI: 10.1016/J.JALGEBRA.2005.11.040
description: scientific article; zbMATH DE number 5078338