Geodesic
Trigonometric Solutions of WDVV Equations and Generalized Calogero–Moser–Sutherland Systems
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Witten–Dijkgraaf–Verlinde–Verlinde equations, $\vee$-systems, Calogero–Moser–Sutherland systems. 
@article{SIGMA_2009_5_a87,
     author = {Misha V. Feigin},
     title = {Trigonometric {Solutions} of {WDVV} {Equations} and {Generalized} {Calogero{\textendash}Moser{\textendash}Sutherland} {Systems}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2009},
     volume = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a87/}
}
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Misha V. Feigin. Trigonometric Solutions of WDVV Equations and Generalized Calogero–Moser–Sutherland Systems. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a87/

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