Anthony Licata

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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 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)
Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the(More)
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