Central extensions of loop groups and obstruction to pre-quantization

Abstract

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.

10 pages, 1 table; v2 contains some improvements as suggested by the reviewer. To appear in Can. Math. Bull