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Determining irreducible $GL(n,K)$-modules

Published online by Cambridge University Press:  15 January 2004

GERALD CLIFF  and
ANNA STOKKE
GERALD CLIFF
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 L. e-mail: gcliff@math.ualberta.ca
ANNA STOKKE
Affiliation:
Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, Manitoba, Canada R3B 2E90. e-mail: a.stokke@uwinnipeg.ca
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Abstract

We discuss several methods which yield spanning sets for the irreducible polynomial $GL(n,K)$-modules, where $K$ is an infinite field. We show that the spanning set which arises from our first method coincides, up to sign, with the spanning set produced by a method due to Pittaluga and Strickland. We prove that these spanning sets are related to the spanning set produced by a third method via the Désarménien matrix.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 1 , January 2004 , pp. 119 - 137
Copyright
2004 Cambridge Philosophical Society

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