Quantum groups and generalized circular elements

Abstract

We show that with respect to the Haar state, the joint distributions of the generators of Van Daele and Wang's free orthogonal quantum groups are modeled by free families of generalized circular elements and semicircular elements in the large (quantum) dimension limit. We also show that this class of quantum groups acts naturally as distributional symmetries of almost-periodic free Araki-Woods factors.

New reference added; a connection to earlier work of S. Vaes on actions of quantum groups on free Araki-Woods factors is pointed out