Delta-matroids and toric degenerations in OG(n,2n+1)

Abstract

We construct an explicit, embedded degeneration of the general torus orbit closure in the maximal orthogonal Grassmannian OG(n,2n+1) into a union of Richardson varieties. In particular, we deduce a formula for the cohomology class of the torus orbit closure, as a sum of products of Schubert classes. The moment map images of the degenerate pieces are the base polytopes of their underlying delta-matroids, and give a polyhedral decomposition of the unit hypercube, which had previously been studied by Chen-Sanchez-Veliz-Ying.