The Mackey bijection via algebraic families of Harish-Chandra modules

יום ד', 17/05/2017 - 10:30
In 1975 George Mackey pointed out an analogy between certain unitary representations of a semisimple Lie group and its Cartan Motion group. 
Recently this analogy was proven to be a part of a bijection between the tempered dual of a real reductive group and the tempered dual of its Cartan Motion group. 
In this talk I will show, in the case of SL(2,R), how algebraic families of Harish-Chandra modules can be used to characterize the Mackey bijection and extend it to an algebraic isomorphism between the admissible duals.