Darboux Coordinates on K-Orbits and the Spectra of Casimir Operators on Lie Groups

Simple item page
dc.creatorShirokov, I. V.
dc.date2001-01-25
dc.date.accessioned2026-07-07T04:28:16Z
dc.date.available2026-07-07T04:28:16Z
dc.descriptionWe 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 $\la$-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.
dc.descriptionLaTeX2e, 15pp, no figures
dc.identifierhttps://arxiv.org/abs/math-ph/0101028
dc.identifierhttp://arxiv.org/abs/math-ph/0101028
dc.identifierTheoretical and Mathematical Physics, Vol. 123, No. 3, 2000
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56724
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.titleDarboux Coordinates on K-Orbits and the Spectra of Casimir Operators on Lie Groups
dc.typetext

Files

Collections

arXiv