Speaker: Jonas Hartwig  (Iowa State University)

Title: Harish-Chandra modules over orders in smash products

Abstract: For an integral domain  Λ with fraction field L, we study a class of noncommutative Λ-orders F in a smash product of L by a Hopf algebra. Specifically we give a sufficient condition for there to be only finitely many isoclasses of simple F-modules that are locally finite for Λ and are supported on a given maximal ideal of Λ. This generalizes a "finiteness of fibers" theorem of Futorny and Ovsienko for Galois orders. We point out some connections to Gelfand-Tsetlin theory for gl_n, Hopf Galois extensions and Cherednik algebras.