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Horizontal partitions and Kleshchev's algorithm

Published online by Cambridge University Press:  24 October 2008

Grant Walker
Grant Walker
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
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Extract

We shall work with rational Mn(K)-modules, where K is an infinite field of prime characteristic p > 0, and Mn(K) is the full matrix semigroup of n × n matrices over K. Recall that equivalence classes of simple rational Mn(K)-modules are parametrized by the set of all partitions λ = (λ1, λ2, …, λl) of length l = l(λ) ≤ n, and that the socle L(λ) of the Schur module (or dual Weyl module) H0(λ) is a simple Mn(K)-module whose highest weight corresponds to the partition λ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 1 , July 1996 , pp. 55 - 60
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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