Singular support for G-categories
Gurbir Dhillon, Joakim F{\ae}rgeman

TL;DR
This paper introduces a notion of singular support for G-categories, characterizes nilpotent G-categories via Whittaker models, and connects these concepts to representation theory and categorification of classical results.
Contribution
It develops a new framework for singular support in G-categories, relates it to Whittaker models, and provides categorified analogues of classical representation theory theorems.
Findings
Characterization of nilpotent G-categories via vanishing of generalized Whittaker models.
Interaction of parabolic induction/restriction with singular support.
Proof of a categorified analogue of Moeglin-Waldspurger and classification of W-algebra modules.
Abstract
For a reductive group , we introduce a notion of singular support for cocomplete dualizable DG-categories equipped with a strong -action. This is done by considering the singular support of the sheaves of matrix coefficients arising from the action. We focus particularly on dualizable -categories whose singular support lies in the nilpotent cone of and refer to these as nilpotent -categories. For such categories, we give a characterization of the singular support in terms of the vanishing of its generalized Whittaker models. We study parabolic induction and restriction functors of nilpotent -categories and show that they interact with singular support in a desired way. We prove that if an orbit is maximal in the singular support of a nilpotent -category , the Hochschild homology of the generalized Whittaker model of …
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Geometry
