Hypertoric category O

Tom Braden*, Anthony Licata, Nicholas Proudfoot, Ben Webster

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1487-1545
Number of pages59
JournalAdvances in Mathematics
Issue number3-4
Publication statusPublished - Oct 2012
Externally publishedYes


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