Hypertoric category O

Abstract

We study the representation theory of the invariant subalgebra of the Weyl algebra under a torus action, which we call a "hypertoric enveloping algebra." We define an analogue of BGG category O for this algebra, and identify it with a certain category of sheaves on a hypertoric variety. We prove that a regular block of this category is highest weight and Koszul, identify its Koszul dual, compute its center, and study its cell structure. We also consider a collection of derived auto-equivalences analogous to the shuffling and twisting functors for BGG category O.

65 pages, TikZ figures (PDF is recommended; DVI will not display correctly on all computers); v5: correcting an error in the proof of Lemma 8.25

References in corpus (1)

• Quantizations of conical symplectic resolutions I: local and global structure

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