The problem of determining the elements of decomposition matrices of symmetric groups
type: Item
instance of: scholarly article
title: The problem of determining the elements of decomposition matrices of symmetric groups
zbMATH Open document ID: 0532.20006
DOI: 10.1007/BF01157460
author: Yu. Yu. Sukhov
published in: Mathematical Notes
publication date: 1983-01-01T00:00:00Z
review text: Let \(D_ n\) be the matrix of decomposition numbers of the symmetric group of degree n over a field of characteristic 2, i.e. the matrix with rows indexed by partitions \(\lambda\) of n and columns indexed by 2- modular representations A of \(S_ n\), in which the (\(\lambda\),A)-entry is equal to the number of composition factors of the Specht module corresponding to \(\lambda\) which are isomorphic to A. The rows of \(D_ n\) for \(\lambda =(n-m,m)\) and \(\lambda =(n-r-1,r,1)\) are known [\textit{G. D. James}, The representation theory of the symmetric groups, Lect. Notes Math. 682 (1978; Zbl 0393.20009)]. The author determines the rows of \(D_ n\) for \(\lambda =(n-m,1,...,1)\).
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 3843986
zbMATH Keywords: decomposition numbers of symmetric group
zbMATH Keywords: partitions
zbMATH Keywords: 2-modular representations
zbMATH Keywords: Specht module
reviewed by: V. D. Mazurov
MaRDI profile type: Publication
cites work: Representations of the symmetric groups over the field of order 2
cites work: Hook representations of the symmetric groups
description: scientific article; zbMATH DE number 3843986