Front: [arXiv:1010.2001] Hypertoric category O

Title: Hypertoric category O
Authors: Tom Braden, Anthony Licata, Nicholas Proudfoot, Ben Webster
Categories: math.RT Representation Theory (math.AG Algebraic Geometry; math.RA Rings and Algebras)
Comments: 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 modules
MSC: 17B10, 16S32, 53D55, 52C35, 14M25
Journal reference: Advances in Mathematics 231 (2012), no. 3-4, 1487-1545

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.

Owner: Ben Webster
Version 1: Mon, 11 Oct 2010 05:44:02 GMT
Version 2: Mon, 13 Jun 2011 06:45:00 GMT
Version 3: Mon, 29 Jul 2013 18:20:17 GMT
Version 4: Mon, 30 Jun 2014 12:39:46 GMT