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Completely Integrable Systems Associated with Classical Root Systems
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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We 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.
Keywords: completely integrable systems; Calogero–Moser systems; Toda lattices with boundary conditions. 
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     author = {Toshio Oshima},
     title = {Completely {Integrable} {Systems} {Associated} with {Classical} {Root} {Systems}},
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Toshio Oshima. Completely Integrable Systems Associated with Classical Root Systems. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a60/

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