Gaussian Generating functionals on easy quantum groups

TL;DR

This paper classifies Gaussian generating functionals on various easy quantum groups, including free unitary, orthogonal, and symplectic types, and explores their centralization and non-Gaussian extensions.

Contribution

It provides a complete description of Gaussian generating functionals on easy quantum groups and introduces a centralization procedure for these functionals.

Findings

Classification of Gaussian generating functionals on easy quantum groups

Characterization of central Gaussian generating functionals

Development of a centralization procedure for generating functionals

Abstract

We describe all Gaussian generating functionals on several easy quantum groups given by non-crossing partitions. This includes in particular the free unitary, orthogonal and symplectic quantum groups. We further characterize central Gaussian generating functionals and describe a centralization procedure yielding interesting (non-Gaussian) generating functionals.