Representation theory of quantizations of the Gieseker moduli space

Gieseker moduli spaces are especially nice and important examples of Nakajima quiver varieties. One can quantize them using quantum Hamiltonian reduction and get associative algebras that generalize type A Rational Cherednik algebras. The latter algebras were extensively studied in the last decade, but the general case has been untouched until very recently. I will explain what I know about the representation theory in the general case. This is based on my work in preparation/in progress.