Integrable system on partial isometries: a finite dimensional picture

TL;DR

This paper explores integrable systems on partial isometries within finite-dimensional spaces, connecting them to the restricted Grassmannian, and provides explicit solutions to these systems.

Contribution

It introduces a finite-dimensional framework for integrable systems on partial isometries related to the restricted Grassmannian, with explicit solutions.

Findings

Explicit solutions to integrable systems on partial isometries.

Connection established between these systems and the restricted Grassmannian.

Finite-dimensional model for a class of integrable systems.

Abstract

The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.