Journal of Generalized Lie Theory and Applications

Centralizers of Commuting Elements in Compact Lie Groups

Kris A Nairn

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Abstract

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

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

Dates
First available in Project Euclid: 3 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1486090825

Digital Object Identifier
doi:10.4172/1736-4337.1000246

Mathematical Reviews number (MathSciNet)
MR3652758

Zentralblatt MATH identifier
06685550

Keywords
Moduli space Lie groups Representation theory Characteristic classes Centralizers

Citation

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. https://projecteuclid.org/euclid.jglta/1486090825


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