Almost commuting elements in compact Lie groups
Group Theory
2007-05-23 v1 High Energy Physics - Theory
Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/9907007,
title = {Almost commuting elements in compact Lie groups},
author = {Armand Borel and Robert Friedman and John W. Morgan},
journal= {arXiv preprint arXiv:math/9907007},
year = {2007}
}
Comments
LaTeX 2e, 141 pages, uses amsfonts.sty, amscd.sty, and XY-Pic. Typeset at least three times