"Character sheaves and Cherednik algebras"

Abstract:


For any algebraic curve C, Etingof introduced  a `global'
Cherednik algebra as a natural deformation of the cross product
of the algebra of differential operators on C^n and the
symmetric group. We provide a construction
of the global Cherednik algebra in terms of quantum
Hamiltonian reduction. We study a category of {em character
D-modules} on a representation scheme associated to C
and define a Hamiltonian reduction functor from that
category to  category O for the global Cherednik algebra.

In the special case of the curve C=C^times, the global Cherednik 
algebra
reduces to the trigonometric Cherednik algebra of type A, and our
character D-modules become  holonomic D-modules on
GL_n \times C^n. The corresponding perverse sheaves  are reminiscent 
of (and include as special cases) Lusztig's character sheaves.

The main result of the paper describes the structure of an
especially important character  D-module on GL_n \times C^n, called
Harish-Chadra D-module.


Victor Ginzburg