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

2004/09/15 by Gan, Wee Liang, Ginzburg, Victor · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0409262

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.

Cited by

• Invariants of finite groups acting on (free) skew fields

Related

• Differential operators and Cherednik algebras
• Cherednik algebras for algebraic curves
• Hamiltonian reduction and nearby cycles for Mirabolic D-modules
• The quantum D-module of product varieties
• Noncommutative Hamiltonian structures and quantizations on preprojective algebras