On the decomposition map for symmetric groups.
type: Item
instance of: scholarly article
title: On the decomposition map for symmetric groups.
zbMATH Open document ID: 1197.20011
author: Karin Erdmann
published in: Journal of Algebraic Combinatorics
publication date: 2009-06-17T00:00:00Z
review text: Let \(R^d\) be the \(\mathbb{Z}\)-module generated by the irreducible characters of the symmetric group \(\mathcal S_d\). In this interesting paper, the author gives a basis for the kernel of the decomposition map in terms of certain symmetric functions. She also proves that when \(F\) has prime characteristic and \(I_{br}^d\) is the kernel of the decomposition map for prime \(p\) then \(R^d/I_{br}^d\otimes_\mathbb{Z} F\) is isomorphic to the radical quotient of the \(p\)-modular Solomon descent algebra.
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 5566030
zbMATH Keywords: irreducible characters
zbMATH Keywords: symmetric groups
zbMATH Keywords: decomposition maps
zbMATH Keywords: Solomon descent algebras
zbMATH Keywords: Brauer characters
zbMATH Keywords: symmetric functions
reviewed by: Hu Jun
MaRDI profile type: Publication
full work available at URL: s10801-008-0134-3
OpenAlex ID: W1986615726
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DOI: 10.1007/S10801-008-0134-3
description: scientific article; zbMATH DE number 5566030