|Location:||MSRI: Simons Auditorium|
Families of representations naturally appear in representation theory of real reductive Lie groups. In my talk I will demonstrate how the Lie groups themselves come in families and how families of representations (of non-isomorphic groups) play a significant role in representation theory. I’ll be focusing on the groups SU(1,1), SU(2) and their Cartan motion group. Furthermore, I will show that there exists an algebraic family of Harish Chandra pairs that is associated with these groups. We shall see how families of Harish Chandra modules relate representations of SU(1,1), SU(2) and their Cartan motion group. These families of HC modules will finally be used to provide some insights into the theory of contraction of representations and the Mackey bijection.
This talk is based on a joint work with Joseph Bernstein and Nigel Higson.