The University of Queensland
Department of Mathematics
Mathematical Physics Seminar
Denominator and numerator expansions for characters of affine Kac-Moody algebras
Professor Ronald C King
Department of Mathematics
University of Southampton
Friday 6 October, 4.00pm
67-111 Priestley Building
It is shown that the character ch V^\lambda of the irreducible representation V^\lambda of highest weight \lambda of an affine Kac-Moody algebra g may be expressed in the form M^\lambda / M , where both the numerator M^\lambda and the denominator M=M^0 may be expanded as an infinite sum of characters of irreducible representations of a maximal simple Lie subalgebra,g_0, of g . The denominator expansions are nothing other than the celebrated Macdonald identities. In the case of the seven infinite series of affine Kac-Moody Lie algebras, indexed by their rank l, each denominator expansion may be rendered in a rank-independent way. This has previously been carried out through the use of Schur function methods, but the same results may be arrived at by making a judicious choice of coset representatives of the affine Weyl group of g with respect to the finite Weyl group of g_0.
All interested are invited to attend.
Enquires to Yao-Zhong Zhang on 3365 2309 or yzz@maths.uq.edu.au