Darboux coordinates onK-orbits and the spectra of Casimir operators on lie groups |
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Authors: | I V Shirokov |
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Institution: | (1) Omsk State University, Omsk, Russia |
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Abstract: | We propose an algorithm for obtaining the spectra of Casimir (Laplace) operators on Lie groups. We prove that the existence
of the normal polarization associated with a linear functional on the Lie algebra is necessary and sufficient for the transition
to local canonical Darboux coordinates (p, q) on the coadjoint representation orbit that is linear in the “momenta.” We show
that the λ-representations of Lie algebras (which are used, in particular, in integrating differential equations) result from
the quantization of the Poisson bracket on the coalgebra in canonical coordinates.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 3, pp. 407–423, June, 2000. |
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