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This article is cited in 11 scientific papers (total in 11 papers)
Completely Integrable Systems Associated with Classical Root Systems
Toshio Oshima Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8914, Japan
Abstract:
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.
Received: December 14, 2006; in final form March 19, 2007; Published online April 25, 2007
Citation:
Toshio Oshima, “Completely Integrable Systems Associated with Classical Root Systems”, SIGMA, 3 (2007), 061, 50 pp.
Linking options:
https://www.mathnet.ru/eng/sigma187 https://www.mathnet.ru/eng/sigma/v3/p61
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Abstract page: | 205 | Full-text PDF : | 54 | References: | 32 |
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