| Résume | Résumé : The Mackey analogy refers to a correspondence between the tempered representation theory of a real reductive group G and that of the associated Cartan motion group G_0. First observed by Mackey in the 1970s, it was turned into a concrete statement by Nigel Higson in 2008 for complex groups and generalized to the real case by Alexandre Afgoustidis in 2016, both works having strong connections with the Connes-Kasparov isomorphism. More recently, joint work with Nigel Higson and Angel Román resulted in the construction of an embedding of the C*-algebra of G_0 into the reduced C*-algebra of G that characterizes the Mackey bijection. In this talk, I will report on joint work with Alexandre Afgoustidis, in which we study the properties of this embedding with respect to certain stratifications (given by families of minimal K-types) and what can be learned from it about in terms of topological properties of the Mackey bijection. |
