Algorithmische Eigenschaften schon Coxeter Schatten

Shadows in Coxeter groups are a well established tool which helps to characterize non-emptiness of double coset intersections in algebraic groups having these Coxeter groups as affine Weyl groups. These intersections in tern are relevant in the context of representation theory or in the study of non-emptiness and dimensions of certain varieties associated to the affine flag variety and affine Grassmannian. This project aims to find closed formulas for and a better algorithmic understanding of shadows.