Gaussian Generating functionals on easy quantum groups
arXiv:2412.00595 · doi:10.1007/s10959-025-01425-w
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.
24 pages, v2 corrects a few minor typos. The final version of the paper will appear in Journal of Theoretical Probability