Cherednik algebras for algebraic curves

Michael Finkelberg; Victor Ginzburg

doi:10.1007/978-0-8176-4697-4_6

Cherednik algebras for algebraic curves

Michael Finkelberg^*
, Victor Ginzburg

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

14 Scopus citations

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)⋊S_n 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 A_n−1, and our character D-modules become holonomic D-modules on GL_n(ℂ)×ℂⁿ. The corresponding perverse sheaves are reminiscent of (and include as special cases) Lusztig’s character sheaves.

Original language	English
Title of host publication	Progress in Mathematics
Publisher	Springer Basel
Pages	121-153
Number of pages	33
DOIs	https://doi.org/10.1007/978-0-8176-4697-4_6
State	Published - 2010
Externally published	Yes

Publication series

Name	Progress in Mathematics
Volume	284
ISSN (Print)	0743-1643
ISSN (Electronic)	2296-505X

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media, LLC 2010.

Keywords

Character sheaves
Cherednik algebras
D–modules

Access to Document

10.1007/978-0-8176-4697-4_6

Cite this

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Cherednik algebras for algebraic curves

Abstract

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Keywords

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