The criterion for tempered spaces, explained in the first lecture, is computable. In this lecture, I will explain how this criterion leads to the classification theory of non-tempered reductive homogeneous spaces by breaking it down into several steps. The technical methods used in the second lecture differ from the dynamical approach presented in the first lecture. Our approach relies on elementary results from finite-dimensional representations and some combinatorics of convex polyhedral cones.
© Toshiyuki Kobayashi