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    Lagrangian fibers in Gelfand-Cetlin systems

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    Attribution 4.0 International
    Author(s)
    Cho, Yunhyung
    Kim, Yoosik
    Oh, Yong-Geun
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    https://hdl.handle.net/2144/29002
    Citation (published version)
    Yunhyung Cho, Y Kim, Yong-Geun Oh. "Lagrangian fibers in Gelfand-Cetlin systems."
    Abstract
    Motivated by the study of Nishinou-Nohara-Ueda on the Floer thoery of Gelfand-Cetlin systems over complex partial flag manifolds, we provide a complete description of the topology of Gelfand-Cetlin fibers. We prove that all fibers are \emph{smooth} isotropic submanifolds and give a complete description of the fiber to be Lagrangian in terms of combinatorics of Gelfand-Cetlin polytope. Then we study (non-)displaceability of Lagrangian fibers. After a few combinatorial and numercal tests for the displaceability, using the bulk-deformation of Floer cohomology by Schubert cycles, we prove that every full flag manifold (n) (n≥3) with a monotone Kirillov-Kostant-Souriau symplectic form carries a continuum of non-displaceable Lagrangian tori which degenerates to a non-torus fiber in the Hausdorff limit. In particular, the Lagrangian S3-fiber in (3) is non-displaceable the question of which was raised by Nohara-Ueda who computed its Floer cohomology to be vanishing.
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    Attribution 4.0 International
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    • BU Open Access Articles [3664]
    • CAS: Mathematics & Statistics: Scholarly Papers [263]


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