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 |
| _version_ | 1818564192160972800 |
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| author | Misha V. Feigin |
| author_facet | Misha V. Feigin |
| author_sort | Misha V. Feigin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T01:25:56Z |
| format | Article |
| id | doaj.art-17070543fa8f49818944ef802a2f36cc |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-14T01:25:56Z |
| publishDate | 2009-09-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-17070543fa8f49818944ef802a2f36cc2022-12-21T23:22:12ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-09-015088Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland SystemsMisha V. FeiginWe 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.http://dx.doi.org/10.3842/SIGMA.2009.088Witten-Dijkgraaf-Verlinde-Verlinde equationsv-systemsCalogero-Moser-Sutherland systems |
| spellingShingle | Misha V. Feigin Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems Symmetry, Integrability and Geometry: Methods and Applications Witten-Dijkgraaf-Verlinde-Verlinde equations v-systems Calogero-Moser-Sutherland systems |
| title | Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems |
| title_full | Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems |
| title_fullStr | Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems |
| title_full_unstemmed | Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems |
| title_short | Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems |
| title_sort | trigonometric solutions of wdvv equations and generalized calogero moser sutherland systems |
| topic | Witten-Dijkgraaf-Verlinde-Verlinde equations v-systems Calogero-Moser-Sutherland systems |
| url | http://dx.doi.org/10.3842/SIGMA.2009.088 |
| work_keys_str_mv | AT mishavfeigin trigonometricsolutionsofwdvvequationsandgeneralizedcalogeromosersutherlandsystems |