Fusion rings for quantum groups
In this paper the authors use tilting modules to study fusion rings for quantum groups at complex roots of unity. In all types, the authors provide an easy method to realize the fusion ring as a quotient of a polynomial ring, in particular, giving an explicit description for generators of the fusion ideal. In types \(A\) and \(C\) this even gives a minimal set of generators, while in other types the situation is more complicated in general. The paper uses crucially the representation theory and combinatorics of affine Weyl groups.
scientific article