Journal of Lie Theory

no. 4
Nonlinear Grassmannians: Plain, Decorated, Augmented
Journal of Lie Theory, Volume 35 (2025) no. 4, pp. 805-843
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.
DOI: 10.5802/jolt.1409
Classification: 58D05, 58D10, 58D15, 53C30, 53D20
Keywords: Nonlinear Grassmannian, coadjoint orbit 
@article{JOLT_2025_35_4_a5,
     author = {S. Haller and C. Vizman},
     title = {Nonlinear {Grassmannians:} {Plain,} {Decorated,} {Augmented}},
     journal = {Journal of Lie Theory},
     pages = {805--843},
     year = {2025},
     volume = {35},
     number = {4},
     doi = {10.5802/jolt.1409},
     zbl = {08124772},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1409/}
}
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S. Haller; C. Vizman. Nonlinear Grassmannians: Plain, Decorated, Augmented. Journal of Lie Theory, Volume 35 (2025) no. 4, pp. 805-843. doi: 10.5802/jolt.1409

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