Ribbon tableaux and q-analogues of fusion rules in WZW conformal field theories

Details Ribbon tableaux and q-analogues of fusion rules in WZW conformal field theories Ribbon tableaux and q-analogues of fusion rules in WZW conformal field theories

1998-10-02

arxiv.org/abs/math/9810008v1

Mathematics

Quantum Algebra

12 pages, Latex, epsf and iop macros. Extended abstract of a talk presented by J.-Y. T. at the conference "Symmetry and Struct

Scientific paper

Starting from known $q$-analogues of ordinary SU(n) tensor products multiplicities, we introduce $q$-analogues of the fusion coefficients of the WZW conformal field theories associated with SU(n). We conjecture combinatorial interpretations of these polynomials, which can be proved in special cases. This allows us to derive in a simple way various kinds of branching functions, the simplest ones being the characters of the minimal unitary series of the Virasoro algebra. We also obtain $q$-analogues of the dimensions of spaces of nonabelian theta functions.

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