Newton–Okounkov bodies of rotated plabic graphs

Establish that all rotations of a plabic graph produce the same Newton–Okounkov body up to unimodular equivalence.

Background

The paper studies the action of the dihedral group on plabic graphs and the Newton–Okounkov bodies associated with these graphs. It proves that reflections can produce Newton–Okounkov bodies that are not unimodularly equivalent to the bodies of the original graphs, using rectangle graphs and their duals as examples.

Against this asymmetry between reflections and rotations, the paper explicitly conjectures that rotation preserves the unimodular-equivalence class of the associated Newton–Okounkov body for every plabic graph. The paper verifies this property for the checkboard and dual checkboard graph orbits but does not establish it in general.