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Australasian Research Symposium on Lie Groups, Algebraic Groups, Quantum Groups, and Their Representations (LAQ'2001)
December 7-10, 2001
The University of Auckland
Auckland, New Zealand

Organizers
Rod Gover (University of Auckland), Vladimir Pestov (Victoria University of Wellington)

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Numerator formulae and coloured partitions for affine Kac-Moody algebras
by
Trevor Welsh
University of Melbourne

By manipulating the Weyl-Kac character formula, we decompose an arbitrary integrable highest weight representation V(L) of an affine Kac-Moody algebra g into irreducible representations of a natural (finite-dimensional) simple Lie subalgebra g_0.

In doing so, we encounter partitions that are coloured in a g-specific way, and discover an elegant means to index the elements of the Coxeter-Weyl group of g using partitions with certain r-cores, where either r or r/2 is the dual Coxeter number of g.

(This is joint work with Prof R.C. King of Southampton University, U.K.)

Date received: November 26, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahw-21.