Jiuzu Hong (UNC-CH), Geometric Methods in Representation Theory Seminar

Title:  Conformal blocks, Verlinde formula and diagram automorphisms

Abstract:  The Verlinde formula computes the dimension of conformal blocks associated to  simple Lie algebras and  Riemann surfaces. If the simple Lie algebra admits a nontrivial diagram automorphism, then this automorphism acts on the space of conformal blocks naturally.  I will report a recent result on the analogue of Verlinde formula for the trace of this automorphism on conformal blocks. Motivated by this formula and Jantzen’s twining formula, I will also give a conjecture on the Verlinde formula for the dimension of conformal blocks associated to twisted affine Lie algebras.