SMS scnews item created by Kevin Coulembier at Mon 29 Apr 2019 1115
Type: Seminar
Distribution: World
Expiry: 24 Jun 2019
Calendar1: 10 May 2019 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Algebra Seminar: Representations of quantized Gieseker varieties and higher rank Catalan numbers
Auth: kevinc@pkevinc.pc (assumed)

# Algebra Seminar: Loseu -- Representations of quantized Gieseker varieties and higher rank Catalan numbers

Ivan Loseu (University of Toronto)

Friday 10 May, 12-1pm, Place: Carslaw 375

Title: Representations of quantized Gieseker varieties and higher rank Catalan numbers

Abstract: 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.


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