Central Extensions of Loop Groups and Obstruction to Pre-Quantization

http://dx.doi.org/10.4153/CMB-2011-131-6
Canad. Math. Bull. 56(2013), 116-126

  Published:2011-06-29
 Printed: Mar 2013

An explicit construction of a pre-quantum line bundle for the moduli space of flat $G$-bundles over a Riemann surface is given, where $G$ is any non-simply connected compact simple Lie group. This work helps to explain a curious coincidence previously observed between Toledano Laredo's work classifying central extensions of loop groups $LG$ and the author's previous work on the obstruction to pre-quantization of the moduli space of flat $G$-bundles.