Twisted conjugacy classes, coadjoint orbits of loop groups and D-branes in the WZW-model

2003/03/31 by Stephan Mohrdieck, Robert Wendt
Mathematics · Physics and Astronomy · #math.QA #hep-th #msc:22E46 #msc:22E67 #msc:81R10

paper · pdf

published as manuscripta math., 114, 531-547 (2004) · 15 pages, totally new version, mistake corrected, to appear under the title "Integral conjugacy classes of compact Lie groups" in Manuscripta Mathematica

arxiv created 2004/01/19 · arxiv updated 2009/11/30

Abstract

We show that untwisted respectively twisted conjugacy classes of a compact and simply connected Lie group which satisfy a certain integrality condition correspond naturally to irreducible highest weight representations of the corresponding affine Lie algebra. Along the way, review the classification of twisted conjugacy classes of a simply connected compact Lie group G and give a description of their stabilizers in terms of the Dynkin diagram of the corresponding twisted affine Lie algebra.

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