Majorization and Spherical Functions

Abstract

Majorization is a partial order on real vectors which plays an important role in a variety of subjects, ranging from algebra and combinatorics to probability and statistics. A basic goal in the study of majorization is to construct functions which characterize this order. In this paper, we introduce a generalized notion of majorization associated to an arbitrary root system Φ, and show that it admits a natural characterization in terms of the values of spherical functions on any Riemannian symmetric space with restricted root system Φ.