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: