@inbook{f8b6722325e7457581566f3b24a21cea,

title = "Cherednik algebras for algebraic curves",

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{\textquoteright}s character sheaves.",

keywords = "Character sheaves, Cherednik algebras, D–modules",

author = "Michael Finkelberg and Victor Ginzburg",

year = "2010",

doi = "10.1007/978-0-8176-4697-4_6",

language = "English",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "121--153",

booktitle = "Progress in Mathematics",

}