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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2008
Hauptverfasser: Caudrelier, V., Crampé, N.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2008
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/147999
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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
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Zusammenfassung: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.
ISSN:1815-0659