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.

# Representations of quantized Giesker varieties and higher rank Catalan numbers

Event time:

Tuesday, April 16, 2019 - 4:00pm

Location:

LOM 201

Speaker:

Ivan Losev

Speaker affiliation:

University of Toronto

Event description: