Nonlinear Grassmannians: Plain, Decorated, Augmented

Decorated and augmented nonlinear Grassmannians can be used to parametrize coadjoint orbits of classical diffeomorphism groups.We provide a general framework for decoration and augmentation functors that facilitates the construction of a smooth structure on decorated or augmented nonlinear Grassmannians.This permits to equip the corresponding coadjoint orbits with the structure of a smooth symplectic Frchet manifold.The coadjoint orbits obtained in this way are not new.Here, we provide a uniform description of their smooth structures.