Centralizers of commuting elements in compact Lie groups
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Publication:510191
zbMATH Open1392.22002arXiv1006.3877MaRDI QIDQ510191
Author name not available (Why is that?)
Publication date: 17 February 2017
Published in: (Search for Journal in Brave)
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, followed by some explicit examples. We conclude by showing that as a result of a compact, connected, simply connected Lie group G having a finite number of subgroups, each conjugate to the centralizer of any element in G, that there is a uniform bound on an irredundant chain of commuting elements.
Full work available at URL: https://arxiv.org/abs/1006.3877
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