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International Mathematics Research Papers (2006) Vol. 2006 : article ID 26439, 54 pages, doi:10.1155/IMRP/2006/26439
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Almost-commuting variety, D-modules, and Cherednik algebras

Wee Liang Gan and Victor Ginzburg

Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA E-mail address: wlgan{at}math.mit.edu
Department of Mathematics, University of Chicago Chicago, IL 60637, USA E-mail address: ginzburg{at}math.uchicago.edu (with an Appendix by Victor Ginzburg)

We study a scheme M closely related to the set of pairs of nxn 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 Mnil sub M. We introduce a category C of D-modules whose characteristic variety is contained in Mnil. Simple objects of that category are analogous to Lusztig's character sheaves. We construct an exact functor of quantum Hamiltonian reduction from our category C to the category O for type-A rational Cherednik algebra.


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