Birkhoff's theorem and convex hulls of Coxeter groups (Q1611847)

Given a finite irreducible Coxeter group \(G\) acting on a finite-dimensional real Euclidean space, the convex hull of \(G\) is a convex polyhedron in the linear space End\((V)\). The authors consider a conjecture proposed by Veronica Zobin concerning the geometry of convex hulls of finite irreducible Coxeter groups. Using the well-known classification of finite irreducible Coxeter groups, the authors can prove the conjecture for many interesting cases. The conjecture, as noted by the authors, can be applied in the theory of operator interpolation in spaces with given symmetry.