Kähler and Poisson Geometry of affine coadjoint orbits of infinite-dimensional unitary groups
Motivated by the study of central extensions of infinite-dimensional unitary groups and their coadjoint orbits, we present families of affine coadjoint orbits of unitary groups that possess natural weak Kähler structures. Some of these orbits possess also a (non-symplectic) Poisson structure inherited form the Poisson-Lie group structure of the corresponding unitary groups. The restricted Grassmannians modeled on Schatten classes $L^p$ will serves as our running example in order to illustrate the different cases depending on $p$. This talk is based on joined works with T. Goliński, G. Larotonda and A. Tahiri.
