We define a toric degeneration of an integrable system on a projective manifold, and prove the existence of a toric degeneration of the Gelfand-Cetlin system on the flag manifold of type A. As an application, we calculate the potential function for a Lagrangian torus fiber of the Gelfand-Cetlin system.
- Gelfand-Cetlin system
- Lagrangian intersection Floer theory
- Toric degeneration
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