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 (v-system) and we determine all trigonometric v-systems w...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2009-09-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.088 |
| 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 (v-system) and we determine all trigonometric v-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 v-system; this inverts a one-way implication observed by Veselov for the rational solutions. |
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| ISSN: | 1815-0659 |