# Symplectic reflection algebras and affine Lie algebras

SPEAKER: Pavel Etingof

TITLE: Symplectic reflection algebras and affine Lie algebras

ABSTRACT: I will present some results and conjectures suggesting that

the representation theory of symplectic reflection algebras for wreath

products (in particular, cyclotomic rational Cherednik algebras) categorifies

certain structures in the representation theory of affine Lie algebras

(namely, decompositions of the restriction of the basic representation

to finite dimensional and affine subalgebras). These conjectures arose

from the insight due to R. Bezrukavnikov and A. Okounkov on the link

between quantum connections for Hilbert schemes of resolutions of Kleinian

singularities and representations of symplectic reflection algebras. Some

of these conjectures were recently proved in the works of Shan-Vasserot

and Gordon-Losev.