Darboux Coordinates on Coadjoint Orbits of Lie Algebras

Details Darboux Coordinates on Coadjoint Orbits of Lie Algebras Darboux Coordinates on Coadjoint Orbits of Lie Algebras

1996-03-05

arxiv.org/abs/solv-int/9603001v1

Lett.Math.Phys. 40 (1997) 41-57

Physics

High Energy Physics

High Energy Physics - Theory

AMSTeX 16pgs

Scientific paper

The method of constructing spectral Darboux coordinates on finite dimensional coadjoint orbits in duals of loop algebras is applied to the one pole case, where the orbit is identified with a coadjoint orbit in the dual of a finite dimensional Lie algebra. The constructions are carried out explicitly when the Lie algebra is $\frak{sl}(2,\bold R),\ \frak{sl}(3, \bold R),$ and $\frak{so}(3, \bold R)$, and for rank two orbits in $\frak{so}(n, \bold R)$. A new feature that appears is the possibility of identifying spectral Darboux coordinates associated to ``dynamical" choices of sections of the associated eigenvector line bundles; i.e. sections that depend on the point within the given orbit.

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