Orbital Integral and $K$-theory Classes

Hang Wang Íõº½  (ECNU)

10:00-11:00, April 3, 2018   Science Building A1510

Abstract:

Consider a semisimple Lie group having discrete series. We use maps from $K$-theory of reduced $C^\ast$-algebra to complex numbers, defined by orbital integrals, to recover information of representations of groups. An important tool is a fixed point formula for equivariant indices of some elliptic operators invariant under the group action. The formula relates geometry and representation in the context of $K$-theory. This is joint work with Peter Hochs.