Symmetries of Spin Calogero Models

Caudrelier, V. & Crampe, N. (2008). Symmetries of Spin Calogero Models. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 4, pp. 1-16. doi: 10.3842/SIGMA.2008.090

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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 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.

Item Type: Article
Uncontrolled Keywords: Calogero models, symmetry algebra, twisted half-loop algebra, MANY-BODY PROBLEM, LONG-RANGE INTERACTIONS, GELFAND-ZETLIN BASES, YANG-BAXTER EQUATION, SIMPLE LIE-ALGEBRAS, ONE DIMENSION, INTEGRABLE SYSTEMS, SUTHERLAND MODEL, GROUND STATE, EXCHANGE
Subjects: Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/161

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