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Symmetries of Spin Calogero Models
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Symmetries of Spin Calogero Models
Інший ID:
2000 Mathematics Subject Classification: 70H06; 81R12; 81R50
Посилання:
Symmetries of Spin Calogero Models / V. Caudrelier, N. Crampé // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ.
Підтримка:
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.
Дата:
2008
Переглядів:
535
Завантажень:
233
Анотація:
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.
