AG Lie-Gruppen: H. Wang, East China Normal University: Exploring the Higher Index Formula: Connections with K-Theory and Representation Theory

Exploring the Higher Index Formula: Connections with K-Theory and Representation Theory – Vortragende: Hang Wang, East China Normal University – Einladender: Kang Li

Abstract: The higher index of an elliptic differential operator, which remains invariant
under a group action, defines a class within the K-theory of the reduced
C*-algebra of the group. Evaluating this higher index typically involves
pairing the index class with cyclic cocycles linked to the group. In the case
of connected reductive groups, specific cyclic cocycles can be defined to
reconstruct representation theory through character formulas. In this talk, I
will explore a higher index formula developed in collaboration with Zijing
Wang, employing geometric methods inspired by the Connes-Moscovici framework.