Open Access
2016 Centralizers of Commuting Elements in Compact Lie Groups
Kris A Nairn
J. Gen. Lie Theory Appl. 10(1): 1-5 (2016). DOI: 10.4172/1736-4337.1000246


The moduli space for a flat G-bundle over the two-torus is completely determined by its holonomy representation. When G is compact, connected, and simply connected, we show that the moduli space is homeomorphic to a product of two tori mod the action of the Weyl group, or equivalently to the conjugacy classes of commuting pairs of elements in G. Since the component group for a non-simply connected group is given by some finite dimensional subgroup in the centralizer of an n-tuple, we use diagram automorphisms of the extended Dynkin diagram to prove properties of centralizers of pairs of elements in G.


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Kris A Nairn. "Centralizers of Commuting Elements in Compact Lie Groups." J. Gen. Lie Theory Appl. 10 (1) 1 - 5, 2016.


Published: 2016
First available in Project Euclid: 3 February 2017

zbMATH: 06685550
MathSciNet: MR3652758
Digital Object Identifier: 10.4172/1736-4337.1000246

Keywords: centralizers , characteristic classes , Lie groups , moduli space , representation theory

Rights: Copyright © 2016 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.10 • No. 1 • 2016
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