Columbia Mathematics Department Colloquium


Finite dimensional irreducible representations over quantizations of symplectic resolutions


Ivan Loseu

(Northeastern University)



A basic problem in Representation theory is, given an algebraic object such as a group, an associative algebra or a Lie algebra, to study its finite dimensional irreducible representations. The first question, perhaps, is how many  there are.

In my talk I will address this question for associative algebras that are quantizations of algebraic varieties admitting symplectic resolutions. Algebras arising this way include universal enveloping algebras of semisimple Lie algebras, as well as W-algebras and symplectic reflection algebras.

The counting problem is a part of a more general program due to Bezrukavnikov and Okounkov relating the representation theory of quantizations to Quantum cohomology of the underlying symplectic varieties. It is also supposed to have other connections to Geometry. I will consider the case of quotient singularities and will make the exposition non-technical.


Wednesday, March 5, 5:00 - 6:00 p.m.
Mathematics 520
Tea will be served at 4:30 p.m.