On categories O for quantized symplectic resolutions

Abstract

In this paper we study categories O over quantizations of symplectic resolutions admitting Hamiltonian tori actions with finitely many fixed points. In this generality, these categories were introduced by Braden, Licata, Proudfoot and Webster. We establish a family of standardly stratified structures (in the sense of the author and Webster) on these categories O. We use these structures to study shuffling functors of Braden, Licata, Proudfoot and Webster (called cross-walling functors in this paper). Most importantly, we prove that all cross-walling functors are derived equivalences that define an action of the Deligne groupoid of a suitable real hyperplane arrangement.

27 pages, v2 36 pages, new material added

References in corpus (2)

• Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras
• Etingof conjecture for quantized quiver varieties II: affine quivers

Cited by in corpus (8)

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• Short Star-Products for Filtered Quantizations, I
• Representations with minimal support for quantized Gieseker varieties
• On modular categories O for quantized symplectic resolutions
• Springer theory for symplectic Galois groups
• Localization theorems for quantized symplectic resolutions