Speaker: Gregor Masbaum
Date: February 02, 2017
Affiliation: CNRS, Paris, France

Abstract: Let $G=\mathrm{Sp}(2n,k)$ be a symplectic group defined over an algebraically closed field $k$ of characteristic $p > 0$. Simple $G$-modules in the natural characteristic can be classified up to isomorphism by highest weights, but their dimensions are largely unknown in general. In this talk, we will present a new family of highest weights for $G$ whose dimensions we can compute explicitly. The corresponding $G$-modules appear as a byproduct of Integral Topological Quantum Field Theory, and their dimensions are given by formulae similar to the Verlinde formula from Conformal Field Theory.