Verlinde algebra

Igor Kříž

Abstract

The level m Verlinde algebra of a compact Lie group G is a commutative ring important in representation theory, mathematical physics, algebraic topology and algebraic geometry. This curious ring also has interesting combinatorial properties: for example, the Verlinde algebra of SU(2) is closely tied to Chebyshev polynomials. In general, calculating in the Verlinde algebra tends to involve interesting combinatorial identities. In this talk, I will define the Verlinde algebra, informally discuss its significance, maybe say in a few words what my Ph.D. student Dan Kneezel and I did with it, and possibly even present some open problems of combinatorial nature.