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Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability (1704.06845v1)
Published 22 Apr 2017 in math.OA, math.CO, and math.GR
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.