Symmetries of Spin Calogero Models
We investigate the symmetry algebras of integrable spin Calogero systems constructed from Dunkl operators associated to finite Coxeter groups. Based on two explicit examples, we show that the common view of associating one symmetry algebra to a given Coxeter group W is wrong. More precisely, the sym...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2008 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147999 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Symmetries of Spin Calogero Models / V. Caudrelier, N. Crampé // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862537607684030464 |
|---|---|
| author | Caudrelier, V. Crampé, N. |
| author_facet | Caudrelier, V. Crampé, N. |
| citation_txt | Symmetries of Spin Calogero Models / V. Caudrelier, N. Crampé // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We investigate the symmetry algebras of integrable spin Calogero systems constructed from Dunkl operators associated to finite Coxeter groups. Based on two explicit examples, we show that the common view of associating one symmetry algebra to a given Coxeter group W is wrong. More precisely, the symmetry algebra heavily depends on the representation of W on the spins. We prove this by identifying two different symmetry algebras for a BL spin Calogero model and three for G₂ spin Calogero model. They are all related to the half-loop algebra and its twisted versions. Some of the result are extended to any finite Coxeter group.
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| first_indexed | 2025-11-24T11:44:39Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147999 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T11:44:39Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Caudrelier, V. Crampé, N. 2019-02-16T16:23:50Z 2019-02-16T16:23:50Z 2008 Symmetries of Spin Calogero Models / V. Caudrelier, N. Crampé // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 70H06; 81R12; 81R50 https://nasplib.isofts.kiev.ua/handle/123456789/147999 We investigate the symmetry algebras of integrable spin Calogero systems constructed from Dunkl operators associated to finite Coxeter groups. Based on two explicit examples, we show that the common view of associating one symmetry algebra to a given Coxeter group W is wrong. More precisely, the symmetry algebra heavily depends on the representation of W on the spins. We prove this by identifying two different symmetry algebras for a BL spin Calogero model and three for G₂ spin Calogero model. They are all related to the half-loop algebra and its twisted versions. Some of the result are extended to any finite Coxeter group. This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. N.C. would like to thank the hospitality of the Centre for Mathematical Science, City University, where this work was initiated. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Symmetries of Spin Calogero Models Article published earlier |
| spellingShingle | Symmetries of Spin Calogero Models Caudrelier, V. Crampé, N. |
| title | Symmetries of Spin Calogero Models |
| title_full | Symmetries of Spin Calogero Models |
| title_fullStr | Symmetries of Spin Calogero Models |
| title_full_unstemmed | Symmetries of Spin Calogero Models |
| title_short | Symmetries of Spin Calogero Models |
| title_sort | symmetries of spin calogero models |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147999 |
| work_keys_str_mv | AT caudrelierv symmetriesofspincalogeromodels AT crampen symmetriesofspincalogeromodels |