AG Lie-Gruppen: H. Wang, East China Normal University: Unveiling the Connes-Kasparov Isomorphism: Bridging K-Theory and Representation of Groups

Unveiling the Connes-Kasparov Isomorphism: Bridging K-Theory and Representation of Groups – Vortragende: Hang Wang, East China Normal University – Einladender: Kang Li

Abstract: The Connes-Kasparov conjecture posits a profound connection between the
K-theory of the reduced C*-algebra of an almost connected group and the
representation ring of its maximal compact subgroup. Serving as a verified
instance of the Baum-Connes conjecture, its implications extend deep into the
realm of representation theory of reductive groups. In fact, this conjecture is
viewed as an operator-theoretic Mackey analogy, with the isomorphism
established through the higher index of twisted Dirac operators on the
homogeneous space associated to the group. In this introductory lecture, we
shall unfold the isomorphism, focusing on the example of a complex semisimple
Lie group.