Majorization and Spherical Functions

2020/06/15 by McSwiggen, Colin, Novak, Jonathan · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2006.08541

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. In this paper, we consider 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.

Cited by

• Majorization via positivity of Jack and Macdonald polynomial differences

Related

• Majorization for Starlike and Convex functions with respect to Conjugate points
• More on the properties of the generalized majorization
• Majorization and Inequalities among Complete Homogeneous Symmetric Functions
• Linear preservers of majorization on ℓ^p(I)
• Symmetric polynomials, p-norm inequalities, and certain functionals related to majorization