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

By Wee Liang Gan, V. Ginzburg. 2004

143 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1a710144f3645082cd64976801524d5d622dda28

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In Algebra and Number Theory

1. I. Losev
2. Pavel Etingof
3. V. Ginzburg
4. R. Bezrukavnikov
5. I. Gordon
6. A. Premet
7. T. Arakawa
8. Michel van den Bergh

In Geometry and Topology

1. I. Losev
2. V. Ginzburg
3. Pavel Etingof
4. R. Bezrukavnikov
5. I. Gordon
6. T. Arakawa
7. Michel van den Bergh
8. E. Gorsky

In Mathematical Physics

1. I. Losev
2. V. Ginzburg
3. Pavel Etingof
4. R. Bezrukavnikov
5. I. Gordon
6. A. Premet
7. T. Arakawa
8. Michel van den Bergh

Citations in the corpus

• LECTURES ON NAKAJIMA'S QUIVER VARIETIES (2009, background): “nd irreducible, moreover, the general point in this scheme is a simple representation of the algebra Πλ. Here, parts (i) and (iii) are due to Crawley-Boevey, [CB1], Theorems 1.1 and 1.2. Part (ii) is [GG], Theorem 3.1. 4.5. Hamiltonian reduction. For any λ∈ CI such that λ·v = 0, the fiber µ−1(λ) is a”
• Isomorphisms of quantizations via quantization of resolutions (2010, methodology): “imaginary root. Set v := nδ,d = ǫ0. Take a generic character θ of GL(v), see the discussion before Proposition 4.2.2. Then there is a C×-equivariant isomorphism X 0 ∼=M 0(DQ,v,d) of schemes (one uses [GG2] to show that the right scheme is reduced and then argues as in the proof of Theorem 11.16 from”
• Parabolic induction and restriction functors for rational Cherednik algebras (2008, methodology): “The difference between Theorem 4.11 and Theorem 6.6.1 of [ GG ] is that in [GG], c is any fixed element ofK, while here c is an indeterminate.”