Monotone Lagrangians in flag varieties
Yunhyung Cho, Yoosik Kim

TL;DR
This paper derives a Maslov index formula for gradient holomorphic discs and uses it to classify all monotone Lagrangian non-toric fibers in Gelfand-Cetlin systems on partial flag manifolds.
Contribution
It introduces a new Maslov index formula for gradient holomorphic discs and applies it to classify monotone Lagrangian fibers in partial flag manifolds.
Findings
Derived a Maslov index formula for gradient holomorphic discs
Classified all monotone Lagrangian non-toric fibers in Gelfand-Cetlin systems
Provided tools for understanding Lagrangian submanifolds in flag varieties
Abstract
In this paper, we give a formula for the Maslov index of a gradient holomorphic disc, which is a relative version of the Chern number formula of a gradient holomorphic sphere for a Hamiltonian -action. Using the formula, we classify all monotone Lagrangian non-toric fibers of Gelfand-Cetlin systems on partial flag manifolds.
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