Hypertoric category O

By Tom Braden, Anthony M. Licata, Nicholas Proudfoot, Ben Webster. 2010

64 citations recorded by the source corpus.

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 .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9b2a622d2e165ffb488cdbf14f55a8369e4769bc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. I. Gordon
2. I. Losev
3. T. Nevins
4. Kevin McGerty
5. Tudor Dimofte
6. D. Gaiotto
7. Mathew Bullimore
8. V. Ginzburg

In Geometry and Topology

1. I. Gordon
2. I. Losev
3. Tudor Dimofte
4. T. Nevins
5. Kevin McGerty
6. D. Gaiotto
7. Mathew Bullimore
8. Sergei Gukov

In Mathematical Physics

1. I. Losev
2. I. Gordon
3. T. Nevins
4. Kevin McGerty
5. Tudor Dimofte
6. D. Gaiotto
7. Mathew Bullimore
8. V. Ginzburg

Citations in the corpus

• The Coulomb Branch of 3d N = 4 Theories (2015, background): “[41, 42](9): first taking a subring of gauge-invariant operators in AH , and then imposing the moment-map constraints”
• On category O for cyclotomic rational Cherednik algebras (2011, methodology): “The definition is inspired by the definition of the category Osph for W-algebras [13], [42], and for hypertoric varieties [10].”
• Derived equivalence for quantum symplectic resolutions (2011, methodology): “ methods of Hodge theory into the representation theory of complex semisimple Lie algebras, with spectacular consequences. More recently, there has been progress (cf. [MV], [GS1], [GS2], [KR], [BKu], [BLPW]) toward a theory of microlocalization, i.e. localization on (an open set of) the quantized co”