Trigonometric solutions of WDVV equations and generalized Calogero-Moser-Sutherland systems

Feigin, M. (2009) Trigonometric solutions of WDVV equations and generalized Calogero-Moser-Sutherland systems. Symmetry, Integrability and Geometry: Methods and Applications, 5, 088. (doi: 10.3842/SIGMA.2009.088)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Feigin, Professor Misha
Authors: Feigin, M.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Symmetry, Integrability and Geometry: Methods and Applications
Journal Abbr.:SIGMA
ISSN (Online):1815-0659

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