Representations of quantized Giesker varieties and higher rank Catalan numbers

Geometry, Symmetry and Physics
Event time: 
Tuesday, April 16, 2019 - 4:00pm
LOM 201
Ivan Losev
Speaker affiliation: 
University of Toronto
Event description: 

A quantized Gieseker variety is an associative algebra quantizing  the global
functions on a Gieseker moduli space. This algebra arises as a quantum Hamiltonian 
reduction of the algebra of differential operators on a suitable space. It depends on
one complex parameter and has interesting and beautiful representation theory. 
For example, when it has finite dimensional representations, there is a unique 
simple one and all finite dimensional representations are completely reducible. 
In fact, this is a part of an ongoing project with Pavel Etingof and Vasily Krylov,
one can explicitly construct the irreducible finite dimensional representation using 
a cuspidal equivariant D-module on sl_n and get an explicit dimension (and character) 
formula. This formula gives a “higher rank” version of rational Catalan numbers. 
I’ll introduce all necessary definitions, describe the resuls mentioned above and, 
time permitting talk about open problems.