Non-connected Lie groups, twisted equivariant bundles and coverings

Weyl’s character formula for non-connected Lie groups and orbital theory for twisted affine Lie algebras

We generalize I. Frenkel’s orbital theory for non twisted affine Lie algebras to the case of twisted affine Lie algebras using a character formula for certain non-connected compact Lie groups.

Equivariant K-Theory of Simply Connected Lie Groups

We compute the equivariant K-theory K∗ G(G) for a simply connected Lie group G (acting on itself by conjugation). We prove that K∗ G(G) is isomorphic to the algebra of Grothendieck differentials on the representation ring. We also study a special example of a nonsimply connected Lie group G, namely PSU(3), and compute the corresponding equivariant K-theory.

The Equivariant Brauer Groups of Principal Bundles

Equivariant Gerbes over Compact Simple Lie Groups

Using groupoid S-central extensions, we present, for a compact simple Lie group G, an infinite dimensional model of S-gerbe over the differential stack G/G whose Dixmier-Douady class corresponds to the canonical generator of the equivariant cohomology H G(G). c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Gerbes Equivariantes sur les groupes de Lie simples compa...

Twisted K–Theory of Lie Groups

I determine the twisted K–theory of all compact simply connected simple Lie groups. The computation reduces via the Freed–Hopkins–Teleman theorem [?] to the CFT prescription, and thus explains why it gives the correct result. Finally I analyze the exceptions noted by Bouwknegt et al [?].