Symplectic Reflection Algebras and Affine Lie Algebras

Symplectic Reflection Algebras and Affine Lie Algebras

These are the notes of my talk at the conference “Double affine Hecke algebras and algebraic geometry” (MIT, May 18, 2010). The goal of this talk is to discuss some results and conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the representation theory for affine Lie algebras. These conjectures arose fr...

Continuous symplectic reflection algebras

The theory of PBW properties of quadratic algebras, to which this paper aims to be a modest contribution, originates from the pioneering work of Drinfeld (see [Dr1]). In particular, as we learned after publication of [EG] (to the embarrassment of two of us!), symplectic reflection algebras and even more general reflection algebras considered in Section 3.6 below, as well as PBW theorems for the...

Symplectic Reflection Algebras

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, with category O, and with spaces of representations of quivers. Mathematics Subject Classification (2000). Primary 16G.

Symplectic Reflection Algebras

Instantons and Affine Lie Algebras *

Various constructions of the affine Lie algebra action on the moduli space of instantons on 4-manifolds are discussed. The analogy between the local-global principle and the role of mass is also explained. The detailed proofs are given in separated papers [16, 17].