Addendum: Specht modules for column-convex diagrams: Characteristic-free results for Weyl modules
type: Item
instance of: scholarly article
title: Addendum: Specht modules for column-convex diagrams: Characteristic-free results for Weyl modules
zbMATH Open document ID: 0877.20007
author: Mark Shimozono
published in: Journal of Algebra
publication date: 1997-12-03T00:00:00Z
review text: Specht modules are used in the construction of the irreducible representations of \(S_n\), the symmetric group on \(n\) letters. Every \(n\)-element subset of the plane \(\mathbb{Z}\times\mathbb{Z}\) is called a diagram and to every diagram \(D\) there corresponds a Specht module \(S^D\). In the previous paper with \textit{V. Reiner} [J. Algebra 174, No. 2, 489-522 (1995; Zbl 0835.20021)], the author gave a composition series for \(S^D\), over fields of characteristic zero, in the cases that \(D\) is column-convex or when \(D\) is the complement of a column-convex diagram. It follows from the Schur-Weyl duality that the analogous results hold for the Weyl module \(K_D\) over a field of characteristic zero. In the paper under review the author shows that these results hold over any commutative ring.
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 16G30
zbMATH DE Number: 1038268
zbMATH Keywords: Specht modules
zbMATH Keywords: irreducible representations
zbMATH Keywords: symmetric groups
zbMATH Keywords: composition series
zbMATH Keywords: column-convex diagrams
zbMATH Keywords: Schur-Weyl duality
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
full work available at URL: jabr.1996.6966
OpenAlex ID: W1968379129
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DOI: 10.1006/JABR.1996.6966
description: scientific article; zbMATH DE number 1038268