Cherednik algebras for algebraic curves

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dc.creatorFinkelberg, Michael
dc.creatorGinzburg, Victor
dc.date2007-04-26
dc.date2008-04-16
dc.date.accessioned2026-07-07T09:32:33Z
dc.date.available2026-07-07T09:32:33Z
dc.descriptionFor any smooth algebraic curve C, Pavel Etingof introduced a `global' Cherednik algebra as a natural deformation of the cross product of the algebra of differential operators on C^n and the symmetric group. We provide a construction of the global Cherednik algebra in terms of quantumn Hamiltonian reduction. We study a category of character D-modules on a representation scheme associated to C and define a Hamiltonian reduction functor from that category to category O for the global Cherednik algebra. In the special case where the curve C is the multiplicative group, the global Cherednik algebra reduces to the trigonometric Cherednik algebra of type A, and our character D-modules become holonomic D-modules on GL_n \times C^n. The corresponding perverse sheaves are reminiscent of (and include as special cases) Lusztig's character sheaves.
dc.descriptionfinal version
dc.identifierhttps://arxiv.org/abs/0704.3494
dc.identifierhttp://arxiv.org/abs/0704.3494
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158816
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.titleCherednik algebras for algebraic curves
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