#### Filter Results:

- Full text PDF available (16)

#### Publication Year

1996

2015

- This year (0)
- Last five years (4)

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- 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)

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)

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)

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)

- Anthony Licata, William H Matthai
- Catheterization and cardiovascular interventions…
- 2002

Prosthetic valve obstruction is a life-threatening complication most commonly caused by thrombus, pannus, or both. We report a St. Jude tricuspid valve obstruction, initially treated with thrombolytic therapy, found to be caused by pannus on pathologic examination. Clinical evaluation and diagnostic evaluation with fluoroscopy and echocardiography in… (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)