Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability
Operator Algebras
2018-08-01 v1 Combinatorics
Group Theory
Abstract
A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) group to arbitrary Coxeter group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability is presented. Characterization of radial and colour-radial functions on dihedral groups and infinite permutation group are shown.
Cite
@article{arxiv.1704.06845,
title = {Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability},
author = {Marek Bożejko and Światosław R. Gal and Wojciech Młotkowski},
journal= {arXiv preprint arXiv:1704.06845},
year = {2018}
}
Comments
26 pages, 2 figures