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Research Article Open Access
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.
Moduli space, Lie groups, Representation theory, Characteristic classes, Centralizers, Algebra, Combinatorics, Deformations Theory, Geometry, Harmonic Analysis, Homological Algebra, Homotopical Algebra, Latin Squares, Lie Theory, Lie Triple Systems, Loop Algebra, Operad Theory, Quantum Group, Quasi-Group, Representation theory, Super Algebras, Lie Superalgebra, Symmetric Spaces, Topologies, Lie Algebra