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Young modules for symmetric groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Karin Erdmann
Karin Erdmann
Affiliation:
Mathematical Institute24-29 St. Giles, Oxford OX1 3LB, United Kingdom, e-mail: erdmann@maths.ox.au.uk
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Abstract

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Let K be a field of characteristic p. The permutation modules associated to partitions of n, usually denoted as Mλ, play a central role not only for symmetric groups but also for general linear groups, via Schur algebras. The indecomposable direct summands of these Mλ were parametrized by James; they are now known as Young modules; and Klyachko and Grabmeier developed a ‘Green correspondence’ for Young modules. The original parametrization used Schur algebras; and James remarked that he did not know a proof using only the representation theory of symmetric groups. We will give such proof, and we will at the same time also prove the correspondence result, by using only the Brauer construction, which is valid for arbitrary finite groups.

MSC classification

Secondary: 20C30: Representations of finite symmetric groups 20C20: Modular representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 2 , October 2001 , pp. 201 - 210
Copyright
Copyright © Australian Mathematical Society 2001

References

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