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arXiv · 0802.0532

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

Misha V. Feigin
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Abstract

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 ($\vee$-system) and we determine all trigonometric $\vee$-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 $\vee$-system; this inverts a one-way implication observed by Veselov for the rational solutions.

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BibTeXRIS

Misha V. Feigin. 2009-09-17. Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems. https://doi.org/10.3842/sigma.2009.088

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