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Completely Integrable Systems Associated with Classical Root Systems
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3, випуск за цей рік
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Completely Integrable Systems Associated with Classical Root Systems
Інший ID:
2000 Mathematics Subject Classification: 81R12; 70H06
Посилання:
Completely Integrable Systems Associated with Classical Root Systems / T. Oshima // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 41 назв. — англ.
Підтримка:
This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’.
Дата:
2007
Переглядів:
432
Завантажень:
253
Анотація:
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 Bn-invariants. We review conditions supporting the conjecture and give a new condition assuring it.
