Potential functions on Grassmannians of planes and cluster transformations

Abstract

With a triangulation of a planar polygon with $n$ sides, one can associate an integrable system on the Grassmannian of 2-planes in an $n$-space. In this paper, we show that the potential functions of Lagrangian torus fibers of the integrable systems associated with different triangulations glue together by cluster transformations. We also prove that the cluster transformations coincide with the wall-crossing formula in Lagrangian intersection Floer theory.

47 pages. v2: revised following referee's comments

References in corpus (3)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Cluster duality and mirror symmetry for Grassmannians
• Lagrangian fibers of Gelfand-Cetlin systems

Cited by in corpus (1)

• Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties