  It was recently proven that the total multiplicity in the decomposition into
irreducibles of the tensor product lambda x mu of two irreducible
representations of a simple Lie algebra is invariant under conjugation of one
of them; at a given level, this also applies to the fusion multiplicities of
affine algebras. Here, we show that, in the case of SU(3), the lists of
multiplicities, in the tensor products lambda x mu and lambda x bar{mu}, are
identical up to permutations. This latter property does not hold in general for
other Lie algebras. We conjecture that the same property should hold for the
fusion product of the affine algebra of su(3) at finite levels, but this is not
investigated in the present paper.
