Hypertoric category O

Tom Braden; Anthony Licata; Nicholas Proudfoot; Ben Webster

doi:10.1016/j.aim.2012.06.019

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arXiv · 1010.2001

Hypertoric category O

Tom Braden·Anthony Licata·Nicholas Proudfoot·Ben Webster

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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.

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BibTeX RIS

Tom Braden, Anthony Licata, Nicholas Proudfoot, Ben Webster. 2010-10-11. Hypertoric category O. https://doi.org/10.1016/j.aim.2012.06.019

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