dorsal/arxiv
View SchemaDarboux Coordinates on Coadjoint Orbits of Lie Algebras
| Authors | M. R. Adams, J. Harnad, J. Hurtubise |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9603001 |
| URL | https://arxiv.org/abs/solv-int/9603001 |
| Journal | Lett.Math.Phys. 40 (1997) 41-57 |
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.
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"abstract": "The method of constructing spectral Darboux coordinates on finite dimensional\ncoadjoint orbits in duals of loop algebras is applied to the one pole case,\nwhere the orbit is identified with a coadjoint orbit in the dual of a finite\ndimensional Lie algebra. The constructions are carried out explicitly when the\nLie algebra is $\\frak{sl}(2,\\bold R),\\ \\frak{sl}(3, \\bold R),$ and\n$\\frak{so}(3, \\bold R)$, and for rank two orbits in $\\frak{so}(n, \\bold R)$. A\nnew feature that appears is the possibility of identifying spectral Darboux\ncoordinates associated to ``dynamical\" choices of sections of the associated\neigenvector line bundles; i.e. sections that depend on the point within the\ngiven orbit.",
"arxiv_id": "solv-int/9603001",
"authors": [
"M. R. Adams",
"J. Harnad",
"J. Hurtubise"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"journal_ref": "Lett.Math.Phys. 40 (1997) 41-57",
"title": "Darboux Coordinates on Coadjoint Orbits of Lie Algebras",
"url": "https://arxiv.org/abs/solv-int/9603001"
},
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