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Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems
Інший ID:
2000 Mathematics Subject Classification: 35Q40; 52C99
Посилання:
Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems / M.V. Feigin // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 16 назв. — англ.
Підтримка:
I am very grateful to L. Hoevenaars, A. Kirpichnikova, M. Pavlov, I. Strachan and A.P. Veselov for useful and stimulating discussions. The work was partially supported by the EPSRC grant EP/F032889/1, by European research network ENIGMA (contract MRTN-CT-2004-5652), by PMI2 Project funded by the UK Department for Innovation, Universities and Skills for the benefit of the Japanese Higher Education Sector and the UK Higher Education Sector.
Дата:
2009
Переглядів:
322
Завантажень:
180
Анотація:
We consider trigonometric solutions of WDVV equations and derive geometric conditions when a collection of vectors with multiplicities determines such a solution. We incorporate these conditions into the notion of trigonometric Veselov system (∨-system) and we determine all trigonometric ∨-systems with up to five vectors. We show that generalized Calogero-Moser-Sutherland operator admits a factorized eigenfunction if and only if it corresponds to the trigonometric ∨-system; this inverts a one-way implication observed by Veselov for the rational solutions.
