Limits of Gaudin Systems: Classical and Quantum Cases
We consider the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new '...
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| Дата: | 2009 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149175 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Limits of Gaudin Systems: Classical and Quantum Cases / A. Chervov, G. Falqui, L. Rybnikov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 34 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1491752019-02-20T01:25:11Z Limits of Gaudin Systems: Classical and Quantum Cases Chervov, A. Falqui, G. Rybnikov, L. We consider the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new ''Gaudin'' algebras (in the quantum case). We will especially treat the case of total collisions, that gives rise to (a generalization of) the so called Bending flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be addressed (in the classical case). We will make use of properties of ''Manin matrices'' to provide explicit generators of the Gaudin Algebras in the quantum case. 2009 Article Limits of Gaudin Systems: Classical and Quantum Cases / A. Chervov, G. Falqui, L. Rybnikov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 34 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 82B23; 81R12; 17B80; 81R50 http://dspace.nbuv.gov.ua/handle/123456789/149175 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 the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new ''Gaudin'' algebras (in the quantum case). We will especially treat the case of total collisions, that gives rise to (a generalization of) the so called Bending flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be addressed (in the classical case). We will make use of properties of ''Manin matrices'' to provide explicit generators of the Gaudin Algebras in the quantum case. |
| format |
Article |
| author |
Chervov, A. Falqui, G. Rybnikov, L. |
| spellingShingle |
Chervov, A. Falqui, G. Rybnikov, L. Limits of Gaudin Systems: Classical and Quantum Cases Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Chervov, A. Falqui, G. Rybnikov, L. |
| author_sort |
Chervov, A. |
| title |
Limits of Gaudin Systems: Classical and Quantum Cases |
| title_short |
Limits of Gaudin Systems: Classical and Quantum Cases |
| title_full |
Limits of Gaudin Systems: Classical and Quantum Cases |
| title_fullStr |
Limits of Gaudin Systems: Classical and Quantum Cases |
| title_full_unstemmed |
Limits of Gaudin Systems: Classical and Quantum Cases |
| title_sort |
limits of gaudin systems: classical and quantum cases |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149175 |
| citation_txt |
Limits of Gaudin Systems: Classical and Quantum Cases / A. Chervov, G. Falqui, L. Rybnikov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 34 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT chervova limitsofgaudinsystemsclassicalandquantumcases AT falquig limitsofgaudinsystemsclassicalandquantumcases AT rybnikovl limitsofgaudinsystemsclassicalandquantumcases |
| first_indexed |
2023-05-20T17:32:30Z |
| last_indexed |
2023-05-20T17:32:30Z |
| _version_ |
1796153528033476608 |