Anthony Licata

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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)
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 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)
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)