  In this note we study asymptotic properties of the *-distribution of traces
of some matrices, with respect to the free Haar trace on the unitary dual
group. The considered matrices are powers of the unitary matrix generating the
Brown algebra. We proceed in two steps, first computing the free cumulants of
any R-cyclic family, then characterizing the asymptotic *-distributions of the
traces of powers of the generating matrix, thanks to these free cumulants. In
particular, we obtain that these traces are asymptotic *-free circular
variables.
