Monotone Lagrangians in Flag Varieties
- 1 November 2019
- journal article
- research article
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2021 (18), 13892-13945
- https://doi.org/10.1093/imrn/rnz227
Abstract
In this paper, we give a formula for the Maslov index of a gradient holomorphic disk, which is a relative version of the Chern number formula of a gradient holomorphic sphere for a Hamiltonian |$S^1$|-action. Using the formula, we classify all monotone Lagrangian fibers of Gelfand–Cetlin systems on partial flag manifolds.Keywords
Funding Information
- National Research Foundation of Korea (NRF-2017R1C1B5018168)
- Institute for Basic Science (IBS-R003-D1)
This publication has 19 references indexed in Scilit:
- Toric degenerations of Gelfand–Cetlin systems and potential functionsAdvances in Mathematics, 2010
- Lagrangian Floer theory on compact toric manifolds, IDuke Mathematical Journal, 2010
- A mirror symmetric construction of qH∗T(G/P)(q)Advances in Mathematics, 2008
- A GKM description of the equivariant cohomology ring of a homogeneous spaceJournal of Algebraic Combinatorics, 2006
- Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifoldsAsian Journal of Mathematics, 2006
- Symplectic cutsMathematical Research Letters, 1995
- Floer cohomology of lagrangian intersections and pseudo‐holomorphic disks ICommunications on Pure and Applied Mathematics, 1993
- The Gelfand-Cetlin system and quantization of the complex flag manifoldsJournal of Functional Analysis, 1983
- Convexity properties of the moment mappingInventiones Mathematicae, 1982
- Convexity and Commuting HamiltoniansBulletin of the London Mathematical Society, 1982