Computing a Birational Invariant for Schubert Varieties Using Representation Theory

This talk focuses on the computation of a certain birational invariant, denoted as β. The core of this work involves analysing the filtration by order of vanishing of global sections of line bundles over a variety. We address this problem for certain Schubert subvarieties of a Grassmannian by using the Borel-Weil-Bott theorem.