Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 088, 10 pages      arXiv:0802.0532

Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems

Misha V. Feigin
Department of Mathematics, University of Glasgow, G12 8QW, UK

Received May 18, 2009, in final form September 07, 2009; Published online September 17, 2009

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.

Key words: Witten-Dijkgraaf-Verlinde-Verlinde equations, ∨-systems, Calogero-Moser-Sutherland systems.

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