Geodesic
Symmetries of Spin Calogero Models
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $B_L$ spin Calogero model and three for $G_2$ 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.
Keywords: Calogero models; symmetry algebra; twisted half-loop algebra. 
@article{SIGMA_2008_4_a89,
     author = {Vincent Caudrelier and Nicolas Cramp\'e},
     title = {Symmetries of {Spin} {Calogero} {Models}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2008},
     volume = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a89/}
}
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Vincent Caudrelier; Nicolas Crampé. Symmetries of Spin Calogero Models. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a89/

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