Representation theory of rational Cherednik algebras
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).