# Generalised Calogero-Moser models and universal Lax pair operators

@article{Bordner1999GeneralisedCM, title={Generalised Calogero-Moser models and universal Lax pair operators}, author={Andrew J. Bordner and E Corrigan and Ryu Sasaki}, journal={Progress of Theoretical Physics}, year={1999}, volume={102}, pages={499-529} }

Calogero-Moser models can be generalised for all of the finite reflection groups. 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 basedon crystallographic root systems, namely those associatedwith Lie algebras. Universal Lax pair operators for all of the generalisedCalogero-Moser mod els andfor any choices of the potentials are constructedas linear…

## 61 Citations

### Universal Lax Pair for Generalised Calogero–Moser Models

- Mathematics
- 2001

Abstract In this talk we introduce generalised Calogero–Moser models and demonstrate their integrability by constructing universal Lax pair operators. These include models based on…

### Calogero-Moser Models. IV ---Limits to Toda Theory---

- Mathematics, Physics
- 1999

Calogero-Moser models and Toda models are well-known integrable multi-particle dynamical systems based on root systems associated with Lie algebras. The relation between these two types of integrable…

### Calogero-Moser Models. II Symmetries and Foldings

- Mathematics
- 1998

Universal Lax pairs (the root type and the minimal type) are presented for CalogeroMoser models based on simply laced root systems, including E8. They exist with and without spectral parameters and…

### Quantum Calogero-Moser models: integrability for all root systems

- Mathematics
- 2000

The issues related to the integrability of quantum Calogero-Moser models based on any root systems are addressed. For the models with degenerate potentials, i.e. the rational with/without the…

### Universal Lax pairs for spin Calogero-Moser models and spin exchange models

- Physics
- 2001

For any root system Δ and a set of vectors which form a single orbit of the reflection (Weyl) group GΔ generated by Δ, a spin Calogero–Moser model can be defined for each of the potentials: rational,…

### On R-matrix valued Lax pairs for Calogero–Moser models

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

The article is devoted to the study of $R$-matrix valued Lax pairs for $N$-body (elliptic) Calogero-Moser models. Their matrix elements are given by quantum ${\rm GL}_{\tilde N}$ $R$-matrices of…

### Calogero-Moser models. V - Supersymmetry and quantum Lax pair -

- Physics
- 2000

It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a…

### Quantum versus classical integrability in Calogero-Moser systems

- Physics
- 2002

Calogero–Moser systems are classical and quantum integrable multiparticle dynamics defined for any root system Δ. The quantum Calogero systems having 1/q2 potential and a confining q2 potential and…

### Polynomials Associated with Equilibrium Positions in Calogero-Moser Systems

- Mathematics
- 2002

In a previous paper (Corrigan–Sasaki), many remarkable properties of classical Calogero and Sutherland systems at equilibrium are reported. For example, the minimum energies, frequencies of small…

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Universal Lax pairs (the root type and the minimal type) are presented for CalogeroMoser models based on simply laced root systems, including E8. They exist with and without spectral parameters and…

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