Geodesic
Nonlinear Grassmannians: Plain, Decorated, Augmented
Stefan Haller1 ; Cornelia Vizman2
1Department of Mathematics, University of Vienna, Austria
2Department of Mathematics, West University of Timisoara, Romania
Journal of Lie Theory, Tome 35 (2025) no. 4, pp. 805-843

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 58D05, 58D10, 58D15, 53C30, 53D20
Mots-clés : Nonlinear Grassmannian, coadjoint orbit

Stefan Haller  1   ; Cornelia Vizman  2

1 Department of Mathematics, University of Vienna, Austria
2 Department of Mathematics, West University of Timisoara, Romania 
Stefan Haller; Cornelia Vizman. Nonlinear Grassmannians: Plain, Decorated, Augmented. Journal of Lie Theory, Tome 35 (2025) no. 4, pp. 805-843. http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a5/
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     title = {Nonlinear {Grassmannians:} {Plain,} {Decorated,} {Augmented}},
     journal = {Journal of Lie Theory},
     pages = {805--843},
     year = {2025},
     volume = {35},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a5/}
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