Department of Mathematics,

Cornell University, USA

E-mail: berest@polygon.math.cornell.edu

**Representation theory of rational Cherednik algebras**

**Abstract:**

The rational Cherednik algebras is a new interesting family of associative
algebras related to a finite Coxeter group. They appear as a natural (`rational')
degeneration of the double-affine Hecke algebras introduced by I. Cherednik,
and the latter may be thought of as a deformation of the former. The rational
Cherednik algebras have a rich representation theory which strikingly resembles
the classical representation theory of semisimple complex Lie algebras.
The purpose of this talk is to present a survey of this theory with a view
towards applications in geometry and mathematical physics.

The talk is based on joint work with Pavel Etingof (MIT) and Victor Ginzburg (Univ. of Chicago).