Fusion algebras for WZW conformal field theories can be computed easily as instances of WeylCharacterRings. The WeylCharacterRing code is modified with an optional parameter k, the level. If k==None the behavior is unchanged. However if k is a positive integer the corresponding fusion ring is created. The reason this works is that the Kac-Walton algorithm for computing the fusion products is closely similar to the Brauer-Klimyk (aka Racah-Speiser) algorithm that is already used by the WeylCharacterRing. One has only to add an affine reflection to make the algorithm compute the fusion product.

I tested this for level 2 in types A2 and B2, comparing with tabulated formulas in Feingold, Fusion Rules for affine Kac-Moody algebras.

A related patch is #15485.

CC: @tscrim @sagetrac-sage-combinat @dwbump

Component: combinatorics

Keywords: Fusion Ring, Verlinde Algebra

Author: Daniel Bump

Branch/Commit: 7546a0d

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/26440