Symplectic reflection algebras and affine Lie algebras

2010/11/20 by Etingof, Pavel
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1011.4584

Abstract

The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products 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.

Related

• Symplectic reflection algebras
• Representations of symplectic reflection algebras and resolutions of deformations of symplectic quotient singularities
• Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
• Poisson orders, symplectic reflection algebras and representation theory
• On some finite dimensional representations of symplectic reflection algebras associated to wreath products