Darboux coordinates on coadjoint orbits of Lie algebras - INSPIRE

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Darboux coordinates on coadjoint orbits of Lie algebras

M.R. Adams
(
- Georgia U.
)
,
John P. Harnad
(
- Concordia U., Math. Dept. and
- Montreal U., CRM
)
,
J. Hurtubise
(
- McGill U.
)

Mar, 1996

16 pages

Published in:

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

e-Print:

solv-int/9603001 [nlin.SI]

DOI:

10.1023/A:1007355508426

Report number:

CRM-2338

View in:

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Abstract:

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.

References(12)

Figures(0)

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)
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