Speaker:
Shamgar Gurevich
Organiser(s):
U of Wisconsin - Madison/MPI
Date:
Tue, 01/07/2014 - 14:00 - 15:00
Given a symplectic vector space V over a finite field (of odd characteristic) one can construct a "quantum" Hilbert space H(L) attached to a Lagrangian subspace L in V. In addition, one can construct a Fourier Transform
F(M,L}: H(L)→H(M),
for every pair of Lagrangians (L,M), such that
F(N,M)F(M,L}=F(N,L),
for every triples (L,M,N) of Lagrangians. This can be used to construct a canonical model H(V) for the famous Weil representation of the symplectic group Sp(V).
In the lecture I will give elementary introduction to the above constructions, and discuss the categorification of these Fourier transforms, what is the related sign problem, and what is its solution. The outcome is a natural category acted by the algebraic group G=Sp, obtaining the categorical Weil representation.
