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...
Збережено в:
| Дата: | 2009 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149132 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149132 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1491322019-02-20T01:26:18Z Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems Feigin, M.V. 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. 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149132 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Feigin, M.V. |
| spellingShingle |
Feigin, M.V. Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Feigin, M.V. |
| author_sort |
Feigin, M.V. |
| title |
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_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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT feiginmv trigonometricsolutionsofwdvvequationsandgeneralizedcalogeromosersutherlandsystems |
| first_indexed |
2023-05-20T17:32:11Z |
| last_indexed |
2023-05-20T17:32:11Z |
| _version_ |
1796153523498385408 |