September 17: Gus Schrader.

Title: Dehn twists and Whittaker functions

Abstract:

The quantum higher Teichmuller theory developed by Fock and Goncharov associates to a hyperbolic marked surface S and a simple Lie group G an infinite dimensional unitary representation of the mapping class group of S. In this talk, I'll describe the solution of the spectral problem for the operators representing Dehn twists in quantum higher Teichmuller theory for G=SL(n) and explain how the Dehn twist eigenfunctions are given by with Whittaker functions for (the modular double of) the quantum group U_q(sl(n)). Joint work with Alexander Shapiro.