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Harish-Chandra bimodules for quantized Slodowy slices. (English) Zbl 1250.17007
Summary: 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.

MSC:
17B08 Coadjoint orbits; nilpotent varieties
14A22 Noncommutative algebraic geometry
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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