Analysis Seminar: "Mackey Analogy in Unitary Representation Theory and in Reduced Group C*-Algebras"

Abstract: In the 1970's, George Mackey proposed an analogy between some unitary representations of a semisimple Lie group and unitary representations of its associated semidirect product group, known as the Cartan motion group. In this talk, I will introduce tempered unitary representations of a reductive Lie group to develop the Mackey analogy. Next, I will define reduced group C*-algebras and show that the reduced group C*-algebra of the Cartan motion group can be embedded into the reduced group C*-algebra of the semisimple group. This can be used to characterize the Mackey analogy. This talk is based on joint work with Nigel Higson where we focused mostly on the complex group.

Host: Walton Green