Amin Tahiri
Dressing actions and symplectic leaves of Banach Poisson Lie groups
In this paper we study the symplectic leaves of a Banach Poisson-Lie group $(G,\mathbb F,\pi)$. We show that the characteristic distribution is a weak distribution , and under the hypothesis that the isotropy subgroups are split Banach Lie subgroups the characteristic distribution is integrable and the leaves are realised by the orbits of the right dressing action. Moreover, the restricted Grassmannian modelled on the Schatten ideal $L_p$ is endowed with a Poisson structure coming from its realisation as a homogeneous space by the Banach Poisson-Lie group $U_{res,p}$.
