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.Comment: 65 pages, TikZ figures (PDF is recommended; DVI will not display correctly on all computers); v3: switched terminology for twisting and shuffling; final version; v4: small correction in definition of standard module