2012/10/06 by Milena Pabiniak, Pabiniak, Milena
Mathematics · #53D #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.SG #msc:53D
paper · pdf · doi:10.48550/arxiv.1210.2000
16 pages, 3 figures
arxiv created 2012/10/06 · openalex publication_date 2012/10/06 · arxiv updated 2012/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In symplectic geometry a question of great importance is whether a (Lagrangian) submanifold is displaceable, that is, if it can be made disjoint from itself by the means of a Hamiltonian isotopy. In these notes we analyze the coadjoint orbits of SU(n) and their Lagrangian submanifolds that are fibers of the Gelfand-Tsetlin map. We use the coadjoint action to displace a large collection of these fibers. Then we concentrate on the case n=3 and apply McDuff's method of probes to show that "most" of the generic Gelfand-Tsetlin fibers are displaceable. "Most" means "all but one" in the non-monotone case, and means "all but a 1-parameter family" in the monotone case. In the case of non-monotone manifold of full flags we present explicitly an unique non-displaceable Lagrangian fiber (S1)3. This fiber was already proved to be non-displaceable in \citeNNU. Our contribution is in displacing other fibers and thus proving the uniqueness.