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- W1765293651 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 (mathcal{D}({C}^{n}) rtimes {mathbb{S}}_{n}) 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 quantum Hamiltonian reduction. We study a category of character (mathcal{D}) -modules on a representation scheme associated with C and define a Hamiltonian reduction functor from that category to category (mathcal{O}) for the global Cherednik algebra. In the special case of the curve (C = {mathbb{C}}^{times }), the global Cherednik algebra reduces to the trigonometric Cherednik algebra of type A n−1,and our character (mathcal{D})-modules become holonomic (mathcal{D})-modules on (G{L}_{n}(mathbb{C}) times {mathbb{C}}^{n}). The corresponding perverse sheaves are reminiscent of (and include as special cases) Lusztig’s character sheaves." @default.
- W1765293651 created "2016-06-24" @default.
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- W1765293651 date "2010-01-01" @default.
- W1765293651 modified "2023-09-24" @default.
- W1765293651 title "Cherednik Algebras for Algebraic Curves" @default.
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- W1765293651 doi "https://doi.org/10.1007/978-0-8176-4697-4_6" @default.
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