"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