On a Certain Stratification of the Gauge Orbit Space

Details On a Certain Stratification of the Gauge Orbit Space On a Certain Stratification of the Gauge Orbit Space

2001-04-18

arxiv.org/abs/math-ph/0104026v1

Physics

Mathematical Physics

12 pages, 1 figure

Scientific paper

For a principal $\rmSU(n)$-bundle over a compact manifold of dimension $2,3,4$, we determine the orbit types of the action of the gauge group on the space of connections modulo pointed local gauge transformations. We find that they are given by Howe subgroups of $\rmSU(n)$ for which a certain characteristic equation is solvable. Depending on the base manifold, this equation leads to a linear, bilinear, or quadratic Diophantine equation.

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