Generating functions for WZNW fusion rules

Abstract

Generating functions for fusion rules of Wess-Zumino-Novikov-Witten (WZNW) models are introduced. First the generating function for the cases su(2) and su(3) are given. We then conjecture a simple structure for the WZNW fusion rules in terms of the finite Lie algebra tensor products. One consequence is that a simple relationship holds between fusion rule generating functions and the corresponding generating functions for tensor product decompositions in finite Lie algebras. Furthermore, our generating functions provide closed and manifestly non-negative formulae for the fusion rules at all integer levels of WZNW models based on a given finite Lie algebra.