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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 9 scientific papers (total in 9 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 (9)
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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 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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