Central extensions of loop groups and obstruction to pre-quantization

2010/04/13 by Derek Krepski, Krepski, Derek
Mathematics · Physics and Astronomy · #22E #53D #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #msc:22E #msc:53D

paper · pdf · doi:10.48550/arxiv.1004.2278

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

arxiv created 2010/09/20 · arxiv updated 2010/09/21

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.

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