Equivariant twisted Real $K$-theory of compact Lie groups

Abstract

Let $G$ be a compact, connected, and simply-connected Lie group viewed as a $G$-space via the conjugation action. The Freed-Hopkins-Teleman Theorem (FHT) asserts a canonical link between the equivariant twisted $K$-homology of $G$ and its Verlinde algebra. In this paper we give a generalization of FHT in the presence of a Real structure of $G$. Along the way we develop preliminary materials necessary for this generalization, which are of independent interest in their own right. These include the definitions of Real Dixmier-Douady bundles, the Real third cohomology group which is shown to classify the former, and Real ${\text{Spin}}^c$ structures.

To appear in Journal of Geometry and Physics

References in corpus (1)

• On groupoids with involutions and their cohomology

Cited by in corpus (2)

• Twisted loop transgression and higher Jandl gerbes over finite groupoids
• Adams operations on twisted $K$-theory of compact Lie groups