Universal Lax Pair for Generalised Calogero­Moser Models

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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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  -