Completely Integrable Systems Associated with Classical Root Systems

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dc.creatorOshima, Toshio
dc.date2005-02-08
dc.date2007-04-25
dc.date.accessioned2026-07-07T09:34:20Z
dc.date.available2026-07-07T09:34:20Z
dc.descriptionWe study integrals of completely integrable quantum systems associated with classical root systems. We review integrals of the systems invariant under the corresponding Weyl group and as their limits we construct enough integrals of the non-invariant systems, which include systems whose complete integrability will be first established in this paper. We also present a conjecture claiming that the quantum systems with enough integrals given in this note coincide with the systems that have the integrals with constant principal symbols corresponding to the homogeneous generators of the $B_n$-invariants. We review conditions supporting the conjecture and give a new condition assuring it.
dc.descriptionThis is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0502028
dc.identifierhttp://arxiv.org/abs/math-ph/0502028
dc.identifierSIGMA 3 (2007), 061, 50 pages
dc.identifierdoi:10.3842/SIGMA.2007.061
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159459
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.subjectExactly Solvable and Integrable Systems
dc.subject81R12; 70H06
dc.titleCompletely Integrable Systems Associated with Classical Root Systems
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