On Specht modules in the Auslander-Reiten quiver
type: Item
instance of: scholarly article
title: On Specht modules in the Auslander-Reiten quiver
zbMATH Open document ID: 0923.20008
author: Thomas Jost
published in: Journal of Algebra
publication date: 1999-09-12T00:00:00Z
review text: Let \(\Lambda\) be a finite-dimensional algebra over a field \(F\). The Auslander-Reiten quiver (AR quiver) \(\Gamma(\Lambda)\) of \(\Lambda\), a certain directed graph on the isomorphism classes of indecomposable \(\Lambda\)-modules, is an important homological invariant of the algebra, and it has been of major use for studying representations. In this paper, we investigate this graph for blocks of \(F{\mathcal S}_n\) where \(F\) is an algebraically closed field of characteristic \(p\), where \(p\) is a non-zero prime dividing \(n!\) and \({\mathcal S}_n\) is the symmetric group of degree \(n\). The aim is to determine the positions of the Specht modules in \(\Gamma(B)\) where \(B\) is a block of \(F{\mathcal S}_n\) of finite or tame representation type or with elementary Abelian defect groups of order \(p^2\).
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 16G60
zbMATH DE Number: 763946
zbMATH Keywords: Auslander-Reiten quivers
zbMATH Keywords: indecomposable modules
zbMATH Keywords: blocks
zbMATH Keywords: symmetric groups
zbMATH Keywords: Specht modules
zbMATH Keywords: tame representation type
zbMATH Keywords: defect groups
zbMATH Keywords: finite representation type
MaRDI profile type: Publication
full work available at URL: jabr.1995.1089
OpenAlex ID: W2034988578
DOI: 10.1006/JABR.1995.1089
description: scientific article; zbMATH DE number 763946