University of Sydney Algebra Seminar

Ivan Loseu (University of Toronto)

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

Representations of quantized Gieseker varieties and higher rank Catalan numbers

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.