Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability

摘要

A new class of positive definite functions related to colour-length functionon arbitrary Coxeter group is introduced. Extensions of positive definitefunctions, called the Riesz-Coxeter product, from the Riesz product on theRademacher (Abelian Coxeter) group to arbitrary Coxeter group is obtained.Applications to harmonic analysis, operator spaces and noncommutativeprobability is presented. Characterization of radial and colour-radialfunctions on dihedral groups and infinite permutation group are shown.