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.
