Families of Dirac operators and quantum affine groups

TL;DR

This paper explores how families of Dirac operators over compact Lie groups can be deformed using quantum group theory, linking twisted K-theory classes to quantum affine algebra representations.

Contribution

It introduces a method to deform Fredholm families of Dirac operators via quantum groups, extending the representation theory framework.

Findings

Deformation of Dirac operator families using quantum affine algebras

Covariant transformation properties under central extensions

Connection between twisted K-theory and quantum group representations

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.