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)

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