Cherednik algebras for algebraic curves

Michael Finkelberg, Victor Ginzburg

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

9 Citations (Scopus)

Abstract

To George Lusztig with admirationFor any algebraic curve C and n≥1, Etingof introduced a “global” Cherednik algebra as a natural deformation of the cross product D(Cn)⋊Sn of the algebra of differential operators on Cn and the symmetric group. We provide a construction of the global Cherednik algebra in terms of quantum Hamiltonian reduction. We study a category of character D-modules on a representation scheme associated with 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×, the global Cherednik algebra reduces to the trigonometric Cherednik algebra of type An−1, and our character D-modules become holonomic D-modules on GLn(ℂ)×ℂn. The corresponding perverse sheaves are reminiscent of (and include as special cases) Lusztig’s character sheaves.

Original languageEnglish
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages121-153
Number of pages33
DOIs
Publication statusPublished - 2010
Externally publishedYes

Publication series

NameProgress in Mathematics
Volume284
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

Keywords

  • Character sheaves
  • Cherednik algebras
  • D–modules

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