Le Groupe Quantique Compact Libre U(n)

Abstract:

The free analogues of U(n) in Woronowicz' theory [Wo2] are the compact matrix quantum groups introduced by Wang and Van Daele. We classify here their irreducible representations. Their fusion rules turn to be related to the combinatorics of Voiculescu's circular variable. If we find an embedding , where A _o (F) is the deformation of SU(2) studied in [B2]. We use the representation theory and Powers' method for showing that the reduced algebras A _u (F) _red are simple, with at most one trace.