Newton-Okounkov bodies and Plucker coordinates

Plucker coordinates provide a concrete and useful way to understand the Grassmannians $Gr(k,n)$ parametrizing k-dimensional subspaces of an n-dimensional vector space. In this talk, we will explore Plucker coordinates for more general homogeneous spaces, and for certain homogeneous spaces, give a representation-theoretic computation to find a family of valuations for which the Plucker coordinates form a Khovanskii basis, and hence correspond to lattice points of a Newton-Okounkov body.

This is joint work in progress with Peter Spacek.