Harish-Chandra bimodules for quantized Slodowy slices

Ginzburg, Victor

doi:10.1090/S1088-4165-09-00355-0

Harish-Chandra bimodules for quantized Slodowy slices
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Represent. Theory 13 (2009), 236-271 Request permission

Abstract:

The Slodowy slice is an especially nice slice to a given nilpotent conjugacy class in a semisimple Lie algebra. Premet introduced noncommutative quantizations 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, to define projective functors, and to construct “noncommutative resolutions” of Slodowy slices via translation functors.

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