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On decomposition numbers and branching coefficients for symmetric and special linear groups

Published online by Cambridge University Press:  01 November 1997

A Kleshchev
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Abstract

In this paper we find the multiplicities $\dim L(\lambda)_{\lambda-\alpha}$ where $\alpha$ is an {\em arbitrary} root and $L(\lambda)$ is an irreducible $SL_n$-module with highest weight $\lambda$. We provide different bases of the corresponding weight spaces and outline some applications to the symmetric groups. In particular we describe certain composition multiplicities in the modular branching rule.

1991 Mathematics Subject Classification: 20C05, 20G05.

Keywords

modular representationssymmetric groupspecial linear groupweight multiplicities
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 75 , Issue 3 , November 1997 , pp. 497 - 558
Copyright
London Mathematical Society 1997

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