The automorphisms of affine fusion rings
  The fusion rings associated to affine Kac-Moody algebras appear in several different contexts in math and mathematical physics. In this paper we find all automorphisms of all affine fusion rings, or equivalently the symmetries of the corresponding fusion coefficients. Most of these are directly related to symmetries of the corresponding Coxeter-Dynkin diagram. We also find all pairs of isomorphic affine fusion rings. 
T. Gannon