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We consider a natural basis of the Iwahori fixed vectors in the Whittaker model of an unramified principal series representation of a split semisimple padic 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)

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(sl2) which are related… (More)

Myocytes that survive in the epicardial border zone of the healing canine infarcted heart provide the substrate for inducible reentrant ventricular arrhythmias. These myocytes have been shown to have altered Ca currents which could impact on Ca homeostasis in these i cells. Objective and Methods: To directly measure and compare intracellular Ca transients… (More)

We introduce the concept of a geometric categorical sl2 action and relate it to that of a strong categorical sl2 action. The latter is a special kind of 2-representation in the sense of Rouquier. The main result is that a geometric categorical sl2 action induces a strong categorical sl2 action. This allows one to apply the theory of strong sl2 actions to… (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 singularity.… (More)

- Tom Braden, Anthony Licata, Nicholas Proudfoot, Ben Webster
- 2015

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)

- 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)

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.

- 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)

- Anthony Licata
- 2008

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