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On categories
${\mathcal{O}}$ for quantized symplectic resolutions
- Part of
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- Journal:
- Compositio Mathematica / Volume 153 / Issue 12 / December 2017
- Published online by Cambridge University Press:
- 07 September 2017, pp. 2445-2481
- Print publication:
- December 2017
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- Article
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In this paper we study categories
${\mathcal{O}}$ over quantizations of symplectic resolutions admitting Hamiltonian tori actions with finitely many fixed points. In this generality, these categories were introduced by Braden et al. We establish a family of standardly stratified structures (in the sense of the author and Webster) on these categories 
${\mathcal{O}}$ . We use these structures to study shuffling functors of Braden et al. (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.
