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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 088, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.088 (Mi sigma434) 		 
This article is cited in 10 scientific papers (total in 10 papers)

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

Misha V. Feigin

Department of Mathematics, University of Glasgow, G12 8QW, UK
Full-text PDF (231 kB) Citations (10)
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DOI: https://doi.org/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 ($\vee$-system) and we determine all trigonometric $\vee$-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 $\vee$-system; this inverts a one-way implication observed by Veselov for the rational solutions.
Keywords: Witten–Dijkgraaf–Verlinde–Verlinde equations, $\vee$-systems, Calogero–Moser–Sutherland systems.
Received: May 18, 2009; in final form September 7, 2009; Published online September 17, 2009
Bibliographic databases:
Document Type: Article
MSC: 35Q40; 52C99
Language: English
Citation: Misha V. Feigin, “Trigonometric Solutions of WDVV Equations and Generalized Calogero–Moser–Sutherland Systems”, SIGMA, 5 (2009), 088, 10 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
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