# The action-angle dual of an integrable Hamiltonian system of Ruijsenaars--Schneider--van Diejen type

## TL;DR

This paper constructs a new integrable many-body model of Ruijsenaars--Schneider--van Diejen type via Hamiltonian reduction, establishing its action-angle duality with deformed Sutherland models, advancing the understanding of integrable systems.

## Contribution

It introduces a novel integrable model of Ruijsenaars--Schneider--van Diejen type through Hamiltonian reduction, linking it to deformed Sutherland models via action-angle duality.

## Key findings

- Derived a new integrable many-body model of Ruijsenaars--Schneider--van Diejen type.
- Established action-angle duality with deformed Sutherland models.
- Extended the framework of Hamiltonian reduction for integrable systems.

## Abstract

Integrable deformations of the hyperbolic and trigonometric ${\mathrm{BC}}_n$ Sutherland models were recently derived via Hamiltonian reduction of certain free systems on the Heisenberg doubles of ${\mathrm{SU}}(n,n)$ and ${\mathrm{SU}}(2n)$, respectively. As a step towards constructing action-angle variables for these models, we here apply the same reduction to a different free system on the double of ${\mathrm{SU}}(2n)$ and thereby obtain a novel integrable many-body model of Ruijsenaars--Schneider--van Diejen type that is in action-angle duality with the respective deformed Sutherland model.