Almost Commuting Elements in Compact Lie Groups

Almost Commuting Elements in Compact Lie Groups

by Armand Borel, Robert S. Friedman, John W. Morgan
     
 

We describe the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in terms of the extended Dynkin diagram of the simply connected cover, together with the coroot integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons

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Overview

We describe the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in terms of the extended Dynkin diagram of the simply connected cover, together with the coroot integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.

Product Details

ISBN-13:
9780821827925
Publisher:
American Mathematical Society
Publication date:
03/19/2002
Series:
Memoirs of the American Mathematical Society Series, #157
Pages:
136

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