Journal of Lie Theory 35 (2025), No. 4, 805--843
Copyright Heldermann Verlag 2025
Nonlinear Grassmannians: Plain, Decorated, Augmented
Stefan Haller
Department of Mathematics, University of Vienna, Austria
stefan.haller@univie.ac.at
Cornelia Vizman
Department of Mathematics, West University of Timisoara, Romania
cornelia.vizman@e-uvt.ro
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 Fréchet manifold. The coadjoint orbits obtained in this way are not new. Here, we provide a uniform description of their smooth structures.
Keywords: Nonlinear Grassmannian, coadjoint orbit.
MSC: 58D05, 58D10, 58D15, 53C30, 53D20.
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