2006-02-24

Farkhod Eshmatov, Cornell University

Quantized Kleinian singularities and Nakajima quiver varieties

To each finite subgroup of SL_2(C) one can associate a family of noncommutative algebras deforming the coordinate ring of the classical Kleinian singularity C^2/\Gamma. In the previous talk (last Fall) we discussed the origin and some homological properties of these algebras. In this talk we will focus on representation theory: specifically, we will explain how to relate classes of projective modules over these algebras to certain irreducible finite-dimensional representations parametrized by Nakajima quiver varieties. The talk will be essentially self-contained; no knowledge from the previous talk will be assumed.