The Totally Nonnegative Grassmannian as a Positive Geometry

The Grassmannian Gr(k,n) has a stratification into positroid varieties which can be indexed by many objects including move-equivalence classes of reduced plabic graphs and bounded affine permutations. Given a bounded affine permutation f, the positroid variety \(\Pi_f\) and the corresponding positroid cell \(\Pi_{f,\geq 0}\) in the TNN Grassmannian form a positive geometry \((\Pi_f, \Pi_{f,\geq 0})\). We will see how to compute the canonical form of a positroid variety using a reduced plabic graph corresponding to that variety.

---

Date published: Wednesday, October 4, 2023