Noncommutative Independence in the Infinite Braid and Symmetric Group

TL;DR

This paper introduces a method combining noncommutative de Finetti results with infinite braid and symmetric group representations to derive factorization properties from symmetries, with applications to group character theory.

Contribution

It presents a new approach merging noncommutative probability with group representations to analyze symmetries and factorization properties.

Findings

Derived factorization properties from symmetries in infinite groups

Developed a constructive procedure for applications

Applied method to group character theory

Abstract

This is an introductory paper about our recent merge of a noncommutative de Finetti type result with representations of the infinite braid and symmetric group which allows to derive factorization properties from symmetries. We explain some of the main ideas of this approach and work out a constructive procedure to use in applications. Finally we illustrate the method by applying it to the theory of group characters.