Gregor Masbaum
CNRS, Paris, France
February 2, 2017
An application of TQFT to modular representation theory: 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.
CNRS, Paris, France
February 2, 2017
An application of TQFT to modular representation theory: 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.