Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems
Mathematical Physics
2009-09-17 v3 math.MP
Exactly Solvable and Integrable 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 (-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.
Keywords
Cite
@article{arxiv.0802.0532,
title = {Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems},
author = {Misha V. Feigin},
journal= {arXiv preprint arXiv:0802.0532},
year = {2009}
}