XLI Workshop on Geometric Methods in Physics Białystok, 1-6.07.2024 XIII School on Geometry and Physics Białystok, 8-12.07.2024

Tomasz Goliński

Integrable system related to restricted Grassmannian on partial isometries

This talk is about a certain hierarchy of integrable bihamiltonian systems constructed on Banach Lie–Poisson spaces related to the restricted Grassmannian $\operatorname{Gr}_\textnormal{res}(\mathcal H)$. This hierarchy was introduced in the paper with A. Odzijewicz by introducing a family of Casimir functions for a pencil of Poisson brackets on the predual space to the central extension of the unitary restricted algebra $\mathfrak u_\textnormal{res}(\mathcal H)$. During the previous Workshop, we realized that under an additional condition this system defines a system of equations in involution on the Banach Lie groupoid of partial isometries. A particular solution will also be presented. This is a joint work with A.B. Tumpach.
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University of Białystok
University of Białystok