Gaussian Generating functionals on easy quantum groups

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

References in corpus (7)

• Quantum Symmetry Groups of Finite Spaces
• Symmetries of Lévy processes on compact quantum groups, their Markov semigroups and potential theory
• Lévy-Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups
• Quantum Brownian Motion on noncommutative manifolds: construction, deformation and exit times
• Hunt's Formula for $S{U}_q(N)$ and $U_q(N)$
• The RFD and KAC quotients of the Hopf*-algebras of universal orthogonal quantum groups
• Connectedness and Gaussian Parts for Compact Quantum Groups