Harish-Chandra bimodules for quantized Slodowy slices

Abstract

The Slodowy slice is an especially nice slice to a given nilpotent conjugacy class in a semisimple Lie algebra. Premet introduced noncommutative quantizaions of the Poisson algebra of polynomial functions on the Slodowy slice. In this paper, we define and study Harish-Chandra bimodules over Premet's algebras. We apply the technique of Harish-Chandra bimodules to prove a conjecture of Premet concerning primitive ideals, and to construct `noncommutative resolutions' of Slodowy slices via translation functors.

Final version to appear in Represent. Theory

References in corpus (4)

• Quantized symplectic actions and W-algebras
• Commutative quotients of finite W-algebras
• On mirabolic D-modules
• Highest weight theory for finite W-algebras

Cited by in corpus (9)

• Lectures on Nakajima's Quiver Varieties
• 2-block Springer fibers: convolution algebras and coherent sheaves
• On the structure of the category O for W-algebras
• Nilpotent orbits and finite W-algebras
• A Localization Theorem for Finite W-algebras
• Singular blocks of parabolic category O and finite W-algebras
• W-algebras at the critical level
• Translation for finite W-algebras
• The Auslander-Gorenstein property for Z-algebras