Almost-commuting variety, D-modules, and Cherednik Algebras
Representation Theory
2007-05-23 v7 Algebraic Geometry
Quantum Algebra
Abstract
We study a scheme M closely related to the set of pairs of n by n-matrices with rank 1 commutator. We show that M is a reduced complete intersection with n+1 irreducible components, which we describe. There is a distinguished Lagrangian subvariety Nil in M. We introduce a category, C, of D-modules whose characteristic variety is contained in Nil. Simple objects of that category are analogous to Lusztig's character sheaves. We construct a functor of Quantum Hamiltonian reduction from category C to the category O for type A rational Cherednik algebra.
Cite
@article{arxiv.math/0409262,
title = {Almost-commuting variety, D-modules, and Cherednik Algebras},
author = {Wee Liang Gan and Victor Ginzburg},
journal= {arXiv preprint arXiv:math/0409262},
year = {2007}
}
Comments
Final version, to appear in IMRN. Introduction expanded, many minor corresctions made, section 7 rewritten, an Appendix added