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arXiv · 2309.10912

From Lagrangian Products to Toric Domains via the Toda Lattice

Yaron Ostrover·Vinicius G. B. Ramos·Daniele Sepe
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Abstract

In this paper we use the periodic Toda lattice to show that certain Lagrangian product configurations in the classical phase space are symplectically equivalent to toric domains. In particular, we prove that the Lagrangian product of a certain simplex and the Voronoi cell of the root lattice $A_n$ is symplectically equivalent to a Euclidean ball. As a consequence, we deduce that the Lagrangian product of an equilateral triangle and a regular hexagon is symplectomorphic to a Euclidean ball in dimension 4.

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Yaron Ostrover, Vinicius G. B. Ramos, Daniele Sepe. 2023-09-19. From Lagrangian Products to Toric Domains via the Toda Lattice. https://doi.org/10.1112/s0010437x24007590

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