Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 104, 18 pages      arXiv:2407.21605      https://doi.org/10.3842/SIGMA.2024.104

Geometry of Integrable Systems Related to the Restricted Grassmannian

Tomasz Goliński a and Alice Barbora Tumpach b
a) University of Białystok, Ciołkowskiego 1M, 15-245 Białystok, Poland
b) Institut CNRS Pauli, UMI CNRS 2842, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

Received August 01, 2024, in final form November 12, 2024; Published online November 22, 2024

Abstract
A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restricted Grassmannian are described, and a momentum map picture is presented.

Key words: integrable systems; momentum map; Banach Lie-Poisson spaces; partial isometries; restricted Grassmannian; Magri method.

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