A non-local Poisson bracket for Coxeter--Toda lattices

E. D. Chuño Vizarreta

We present a non-local Poisson bracket defined on the phase space $G^{u,v}/H$ of a Coxeter--Toda lattice, where $G^{u,v}$ is a Coxeter double Bruhat cell of $G{L}_n$ and $H$ is the s…