Hypertoric category O
Representation Theory
2022-11-18 v5 Algebraic Geometry
Rings and Algebras
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.
Cite
@article{arxiv.1010.2001,
title = {Hypertoric category O},
author = {Tom Braden and Anthony Licata and Nicholas Proudfoot and Ben Webster},
journal= {arXiv preprint arXiv:1010.2001},
year = {2022}
}
Comments
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