Multiplicative integrable models from Poisson-Nijenhuis structures

TL;DR

This paper explores how Poisson-Nijenhuis geometry can be used to construct multiplicative integrable models on symplectic groupoids, linking integrability with groupoid structures and providing explicit examples on symmetric spaces.

Contribution

It demonstrates that maximal rank Poisson-Nijenhuis structures naturally induce multiplicative integrable models compatible with symplectic groupoids.

Findings

Maximal rank PN structures define multiplicative integrable models.

Examples provided on compact hermitian symmetric spaces.

The set of contour levels inherits a topological groupoid structure.

Abstract

We discuss the role of Poisson-Nijenhuis geometry in the definition of multiplicative integrable models on symplectic groupoids. These are integrable models that are compatible with the groupoid structure in such a way that the set of contour levels of the hamiltonians in involution inherits a topological groupoid structure. We show that every maximal rank PN structure defines such a model. We consider the examples defined on compact hermitian symmetric spaces and studied in [arXiv:1503.07339].