Abstract
Let P → M be a principal G-bundle with connection 1-form θ and curvature Θ. For a subset S of g* the given connection is S-fat (Weinstein, [5]) if for every μ in S the form μ ° Θ is nondegenerate on each horizontal subspace in TP.
Let K be a compact group and K/H be its coadjoint orbit. The orthogonal projection t → h defines a connection on the principal H-bundle K → K/H. We show that this connection is fat off certain walls of Weyl chambers in h*. We then apply the result to the construction of symplectic fiber bundles over K/H. As an example, we show how higher-dimensional coadjoint orbits fiber symplectically over lower-dimensional orbits.
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Lerman, E. How fat is a fat bundle?. Lett Math Phys 15, 335–339 (1988). https://doi.org/10.1007/BF00419591
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DOI: https://doi.org/10.1007/BF00419591