How fat is a fat bundle?

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)335-339
Number of pages5
JournalLetters in Mathematical Physics
Volume15
Issue number4
DOIs
StatePublished - May 1 1988
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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