Caudrelier, V. and Crampe, N. (2008). Symmetries of Spin Calogero Models. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 4, pp. 116. doi: 10.3842/SIGMA.2008.090
Abstract
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 G(2) spin Calogero model. They are all related to the halfloop algebra and its twisted versions. Some of the result are extended to any finite Coxeter group.
Publication Type:  Article 

Publisher Keywords:  Calogero models, symmetry algebra, twisted halfloop algebra, MANYBODY PROBLEM, LONGRANGE INTERACTIONS, GELFANDZETLIN BASES, YANGBAXTER EQUATION, SIMPLE LIEALGEBRAS, ONE DIMENSION, INTEGRABLE SYSTEMS, SUTHERLAND MODEL, GROUND STATE, EXCHANGE 
Subjects:  Q Science > QC Physics 
Departments:  School of Mathematics, Computer Science & Engineering > Mathematics 
URI:  https://openaccess.city.ac.uk/id/eprint/161 

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