Fusion rules and the Patera-Sharp generating-function method

Abstract

We review some contributions on fusion rules that were inspired by the work of Sharp, in particular, the generating-function method for tensor-product coefficients that he developed with Patera. We also review the Kac-Walton formula, the concepts of threshold level, fusion elementary couplings, fusion generating functions and fusion bases. We try to keep the presentation elementary and exemplify each concept with the simple su(2) k case.

Polytope sums and Lie characters

“…This author was introduced to polytope theory in different contexts -in the study of tensor product multiplicities and the related affine fusion multiplicities (see [14] and references therein, and [4]), the fusion of Wess-Zumino-Witten conformal field theories. It would be interesting to consider applications of the Brion formula in those subjects.…”

“…As an extremely simple example, consider the one-dimensional lattice polytope with vertices (2) and (7). Its exponential sum is (1.4) e (7) + e (6) + e (5) + e (4) + e (3) + e (2) . As a very simple example, consider the lattice polytope in Z 2 with vertices (0, 0), (1,0) and (1,1).…”