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 (∨-system) and we determine all trigonometric ∨-systems w...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149132 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems / M.V. Feigin // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-149132 |
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Feigin, M.V. 2019-02-19T17:35:38Z 2019-02-19T17:35:38Z 2009 Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems / M.V. Feigin // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 16 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35Q40; 52C99 https://nasplib.isofts.kiev.ua/handle/123456789/149132 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. I am very grateful to L. Hoevenaars, A. Kirpichnikova, M. Pavlov, I. Strachan and A.P. Veselov for useful and stimulating discussions. The work was partially supported by the EPSRC grant EP/F032889/1, by European research network ENIGMA (contract MRTN-CT-2004-5652), by PMI2 Project funded by the UK Department for Innovation, Universities and Skills for the benefit of the Japanese Higher Education Sector and the UK Higher Education Sector. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems |
| spellingShingle |
Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems Feigin, M.V. |
| title_short |
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_sort |
trigonometric solutions of wdvv equations and generalized calogero-moser-sutherland systems |
| author |
Feigin, M.V. |
| author_facet |
Feigin, M.V. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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 (∨-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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149132 |
| citation_txt |
Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems / M.V. Feigin // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 16 назв. — англ. |
| work_keys_str_mv |
AT feiginmv trigonometricsolutionsofwdvvequationsandgeneralizedcalogeromosersutherlandsystems |
| first_indexed |
2025-12-07T18:57:15Z |
| last_indexed |
2025-12-07T18:57:15Z |
| _version_ |
1850876976204611584 |