Harish-Chandra bimodules over quantized symplectic singularities

DOI10.1007/S00031-020-09638-5arXiv1810.07625MaRDI QIDQ6308407

Author name not available (Why is that?)

Publication date: 17 October 2018

Abstract: In this paper we classify the irreducible Harish-Chandra bimodules with full support over filtered quantizations of conical symplectic singularities under the condition that none of the slices to codimension 2 symplectic leaves has type

E_{8}

. More precisely, we show that the top quotient

o v e r l i n e o p e r a t o r n a m e H C (m a t h c a l A_{l} a m b d a)

of the category of Harish-Chandra bimodules over the quantization

m a t h c a l A_{l} a m b d a

with parameter

l a m b d a

embeds into the category of representations of the algebraic fundamental group,

G a m m a

, of the open leaf. The image coincides with the representations of

G a m m a / G a m m a_{l} a m b d a

, where

G a m m a_{l} a m b d a

is a normal subgroup of

G a m m a

that can be recovered from the quantization parameter

l a m b d a

. As an application of our results, we describe the Lusztig quotient group in terms of the geometry of the normalization of the orbit closure in almost all cases.

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