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- ANTHONY LICATA
- 2009

We categorify the R-matrix isomorphism between tensor products of minuscule representations of Uq(sln) by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of Uq(sl 2) which are related… (More)

- Ben Brubaker, Anthony Licata
- 2012

We consider a natural basis of the Iwahori fixed vectors in the Whittaker model of an unramified principal series representation of a split semisimple p-adic group, indexed by the Weyl group. We show that the elements of this basis may be computed from one another by applying Demazure-Lusztig operators. The precise identities involve correction terms, which… (More)

- ANTHONY LICATA
- 2009

We introduce the concept of a geometric categorical sl 2 action and relate it to that of a strong categorical sl 2 action. The latter is a special kind of 2-representation in the sense of Rouquier. The main result is that a geometric categorical sl 2 action induces a strong categorical sl 2 action. This allows one to apply the theory of strong sl 2 actions… (More)

We construct an equivalence of categories from a strong categorical sl(2) action, following the work of Chuang-Rouquier. As an application, we give an explicit, natural equivalence between the derived categories of coherent sheaves on cotangent bundles to complementary Grassmannians.

We define and study category O for a symplectic resolution, generalizing the classical BGG category O, which is associated with the Springer resolution. This includes the development of intrinsic properties paralleling the BGG case, such as a highest weight structure and analogues of twisting and shuffling functors, along with an extensive discussion of… (More)

In this expository paper we present an overview of various graphical categorifications of the Heisenberg algebra and its Fock space representation. We begin with a discussion of " weak " categorifications via modules for Hecke algebras and " geometrizations " in terms of the cohomology of the Hilbert scheme of points on the resolution of a simple… (More)

- Tom Braden, Anthony Licata, Christopher Phan, Nicholas Proudfoot, Ben Webster
- 2009

We show that the center of a flat graded deformation of a standard Koszul algebra A behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed-point set. In particular, the center of A acts by characters on the deformed standard modules, providing a " localization map. " We construct a universal graded… (More)

- Tom Braden, Anthony Licata, Christopher Phan
- 1996

We show that the center of a flat graded deformation of a standard Koszul algebra behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed-point set. In particular, the center acts by characters on the deformed standard modules, providing a " localization map ". We construct a universal graded deformation,… (More)

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… (More)

- ANTHONY LICATA
- 2008

We define complexes of vector bundles on products of moduli spaces of framed rank r torsion-free sheaves on P 2. The top non-vanishing equivariant Chern classes of the cohomology of these complexes yield actions of the r-colored Heisen-berg and Clifford algebras on the equivariant cohomology of the moduli spaces. In this way we obtain a geometric… (More)