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FAMILIES OF DIRAC OPERATORS AND QUANTUM AFFINE GROUPS

Published online by Cambridge University Press:  31 May 2011

JOUKO MICKELSSON*
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland Department of Theoretical Physics, Royal Institute of Technology, Stockholm, Sweden (email: [email protected])
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Abstract

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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 paper we 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 transforms covariantly under a central extension of the algebra.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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