  In this article we give examples which show that the TQFT representations of
the mapping class groups derived from quantum SU(N) for N>2 are generically
decomposable. One general decomposition of the representations is induced by
the symmetry which exchanges SU(N) representation labels by their conjugates.
The respective summands of a given parity are typically still reducible into
many further components.
  Specifically, we give an explicit basis for an irreducible direct summand in
the SL(2,Z) representation obtained from quantum PSU(3) when the order of the
root of unity is a prime r=2 mod 3. We show that this summand is isomorphic to
the respective PSU(2) representation.
