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

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 w...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2009
Main Author: Feigin, M.V.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149132
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems / M.V. Feigin // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 16 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Description
Summary: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.
ISSN:1815-0659