Journal of Generalized Lie Theory and Applications

Centralizers of Commuting Elements in Compact Lie Groups

Kris A Nairn

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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.

Article information

J. Gen. Lie Theory Appl., Volume 10, Number 1 (2016), 5 pages.

First available in Project Euclid: 3 February 2017

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Moduli space Lie groups Representation theory Characteristic classes Centralizers


Nairn, Kris A. Centralizers of Commuting Elements in Compact Lie Groups. J. Gen. Lie Theory Appl. 10 (2016), no. 1, 5 pages. doi:10.4172/1736-4337.1000246.

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