Almost-commuting variety, D-modules, and Cherednik Algebras

Wee Liang Gan; Victor Ginzburg

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arXiv · math/0409262

Almost-commuting variety, D-modules, and Cherednik Algebras

Wee Liang Gan·Victor Ginzburg

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Abstract

We study a scheme M closely related to the set of pairs of n by n-matrices with rank 1 commutator. We show that M is a reduced complete intersection with n+1 irreducible components, which we describe. There is a distinguished Lagrangian subvariety Nil in M. We introduce a category, C, of D-modules whose characteristic variety is contained in Nil. Simple objects of that category are analogous to Lusztig's character sheaves. We construct a functor of Quantum Hamiltonian reduction from category C to the category O for type A rational Cherednik algebra.

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BibTeX RIS

Wee Liang Gan, Victor Ginzburg. 2005-12-14. Almost-commuting variety, D-modules, and Cherednik Algebras. https://arxiv.org/abs/math/0409262

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