Skip to main content

Families of Dirac operators and affine quantum groups

Posted in
Speaker: 
Jouko Mickelsson
Affiliation: 
Helsinki
Date: 
Mon, 21/06/2010 - 11:00 - 12:00
Location: 
MPIM Lecture Hall

Families of Dirac type operators constructed from the supersymmetric Wess-Zumino-Witten model are a useful tool in Fredholm operator realization of twisted K-theory classes on compact Lie groups. They transform in a covariant manner with respect to the action of a central extension of a loop group, the level of the representation giving directly the Dixmier-Douady class of the twisting gerbe. I want to describe a deformation of this system in the language of quantum affine algebras. The loop group covariance property is replaced by a "infinitesimal" Hopf algebra covariance with respect to a quantum enveloping algebra $U_q(\hat g)$ and the Dixmier-Douady class is defined purely algebraically from the action of a central group like element in the Hopf algebra. This is a ongoing project with Antti Harju.
 

AttachmentSize
File Mickelsson_Bonn10.pdf215.48 KB
© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A