Symmetry, Integrability and Geometry: Methods and Applications (Sep 2009)
Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems
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 (v-system) and we determine all trigonometric v-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 v-system; this inverts a one-way implication observed by Veselov for the rational solutions.
