# Calogero-Sutherland system with two types interacting spins

## TL;DR

This paper extends the classical Calogero-Sutherland system to include two types of interacting spins, demonstrating its integrability through a Lax pair and r-matrix construction within the Hitchin framework.

## Contribution

It introduces a new integrable model with two interacting spin types and provides a Lax representation and r-matrix formulation for the system.

## Key findings

- Model reduces to standard Calogero-Sutherland when one spin type vanishes
- Complete integrability is established via Lax pair and r-matrix
- Spectral parameter is defined on a singular curve

## Abstract

We consider the classical Calogero-Sutherland system with two types of interacting spin variables. It can be reduced to the standard Calogero-Sutherland system, when one of the spin variables vanishes. We describe the model in the Hitchin approach and prove complete integrability of the system by constructing the Lax pair and the classical $r$-matrix with the spectral parameter on a singular curve.