Families of Dirac operators and quantum affine groups

Abstract

Twisted K-theory classes over compact Lie groups can be realized as families of Fredholm operators using the representation theory of loop groups. In this talk I want to show how to deform the Fredholm family, in the sense of quantum groups. The family of Dirac type operators is parametrized by vectors in the adjoint module for a quantum affine algebra and transform covariantly under a (central extension of) the algebra.