|Title||Real K-theory of compact Lie groups|
|Presenter||Chi-Kwong Fok (The University of Adelaide)|
|Author(s)||Dr Chi-Kwong Fok|
|Session||Category Theory, Algebraic Topology, K-Theory|
Let $G$ be a compact connected Lie group, viewed as a $G$-space via the conjugation action. A theorem of Brylinski--Zhang states that the equivariant K-theory of $G$ is the ring of K\"ahler differentials of its complex representation ring, while a recent deep theorem by Freed--Hopkins--Teleman asserts a canonical isomorphism between the twisted equivariant version and the Verlinde algebra of $G$. In this talk, I will present generalizations of both results in the context of Atiyah's Real K-theory.