
SIGMA 5 (2009), 088, 10 pages arXiv:0802.0532
http://dx.doi.org/10.3842/SIGMA.2009.088
Trigonometric Solutions of WDVV Equations and Generalized CalogeroMoserSutherland 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
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
(∨system) and we determine all trigonometric ∨systems with
up to five vectors. We show that generalized
CalogeroMoserSutherland operator admits a factorized eigenfunction
if and only if it corresponds to the trigonometric ∨system; this inverts a oneway implication observed by Veselov for the rational solutions.
Key words:
WittenDijkgraafVerlindeVerlinde equations, ∨systems, CalogeroMoserSutherland systems.
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