Toric degenerations of Gelfand-Cetlin systems and potential functions

Abstract

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.

54 pages, 8 figures. v2: added section 4, revised section 9, and minor changes here and there