Polypositroids is a class of convex polytopes defined to be those polytopes that are simultaneously generalized permutohedra (or polymatroids) and alcoved polytopes. Whereas positroids are the matroids arising from the totally nonnegative Grassmannian,polypositroids are "positive" polymatroids. We parametrize polypositroids using Coxeter necklaces and balanced graphs, and describe the cone of polypositroids by extremal rays and facet inequalities. We generalize polypositroids to an arbitrary finite Weyl group W, and connect them to cluster algebras and to generalized associahedra. We also discuss membranes, which are certain triangulated surfaces. They extend the notion of plabic graphs from positroids to polypositroids. The talk is based on a joint work with Thomas Lam.
Time & Location
Jun 14, 2021 | 04:30 PM