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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.