ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: Mathieu, Pierre, Département de physique, Universté Laval, Québec, Canada, G1K 7P4 Generating functions for fusion rules A fusion rule is a well defined rule for decomposing the product of two integrable highest-weight representation of a given affine Lie algebra at a fixed level k into a direct sum of integrable representations. It can be regarded as a restricted tensor product for the corresponding Lie algebras finite weights, with the degree of truncation determined by the level k. Fusion coefficients are thus specified in terms of tensor-product coefficients and threshold levels. Expressions for the threhold level can be obtained, for instance, in terms of Berenstein-Zelevinsky triangles for su(N). Generating functions describing the fusion rules of low rank affine Lie algebras and presented.