Equivariant K-theory of compact Lie groups with involution

Abstract

For a compact simply connected simple Lie group $G$ with an involution $\alpha$, we compute the $G⋊\mathbb{Z}/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\mathbb{Z}/2$ acts either by $\alpha$ or by $g\mapsto \alpha (g{)}^{-1}$. We also give a representation-theoretic interpretation of those groups, as well as of $K_G(G)$.

Accepted for publication in Journal of K-theory

References in corpus (1)

• On the definition and K-theory realization of a modular functor