REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Ted Stadnik

ABSTRACT: This talk will discuss recent research in localization for the hypertoric enveloping algebra in positive characteristic.   As a prototypical example of positive characteristic localization and its usefulness, the talk will examine results from localization for semisimple Lie algebras due to Bezrukavnikov, Mirkovic, and Rumynin.  I will also discuss the algebraic construction of hypertoric varieties (also known as toric hyperkahler manifolds) and the analogues of BMR's results there.  I will compare and contrast the proofs and the constructions of both situations.  For example, it is a difficult problem to determine splitting bundles on the fibers of the moment map in the case of Lie algebras.  In the case of hypertoric varieties, one can use a result of Ogus-Vologodsky to realize the splitting bundle on fibers as canonically determined by a natural lift of Frobenius.