## Toric degenerations of integrable systems on Grassmannians and polygon spaces.(English)Zbl 1304.37037

Authors’ abstract: We introduce a completely integrable system on the Grassmannian of $$2$$-planes in an $$n$$-space associated with any triangulation of a polygon with $$n$$ sides, and we compute the potential function for its Lagrangian torus fiber. The moment polytopes of this system for different triangulations are related by an integral piecewise-linear transformation, and the corresponding potential functions are related by its geometric lift in the sense of Berenstein and Zelevinsky.

### MSC:

 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 53D37 Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category 53D12 Lagrangian submanifolds; Maslov index 14M15 Grassmannians, Schubert varieties, flag manifolds
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### References:

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