Journal of Nonlinear Mathematical Physics

Volume 8, Issue Supplement, February 2001, Pages 254 - 260

Universal Lax Pair for Generalised Calogero­Moser Models

Authors
R. Sasaki
Corresponding Author
R. Sasaki
Available Online 1 February 2001.
DOI
10.2991/jnmp.2001.8.s.44How to use a DOI?
Abstract

In this talk we introduce generalised Calogero­Moser models and demonstrate their integrability by constructing universal Lax pair operators. These include models based on non-crystallographic root systems, that is the root systems of the finite reflection groups, H3, H4, and the dihedral group I2(m), besides the well-known ones based on crystallographic root systems, namely those associated with Lie algebras. Universal Lax pair operators for all of the generalised Calogero­Moser models and for any choices of the potentials are linear combinations of the reflection operators. The equivalence of the Lax pair with the equations of motion is proved by decomposing the root system into a sum of two-dimensional sub-root systems, A2, B2, G2, and I2(m). The root type and the minimal type Lax pairs, derived in our previous papers, are given as the simplest representations. The spectral parameter dependence plays an important role in the Lax pair operators, which bear a strong resemblance to the Dunkl operators.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
8 - Supplement
Pages
254 - 260
Publication Date
2001/02/01
ISBN
91-631-0262-5
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2001.8.s.44How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - R. Sasaki
PY  - 2001
DA  - 2001/02/01
TI  - Universal Lax Pair for Generalised Calogero­Moser Models
JO  - Journal of Nonlinear Mathematical Physics
SP  - 254
EP  - 260
VL  - 8
IS  - Supplement
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2001.8.s.44
DO  - 10.2991/jnmp.2001.8.s.44
ID  - Sasaki2001
ER  -