  The phenomenology of the scaling behavior of higher order structure functions
of velocity differences across a scale $R$ in turbulence should be built around
the irreducible representations of the rotation symmetry group. Every
irreducible representation is associated with a scalar function of $R$ which
may exhibit different scaling exponents. The common practice of using moments
of longitudinal and transverse fluctuations mixes different scalar functions
and therefore may mix different scaling exponents. It is shown explicitly how
to extract pure scaling exponents for correlations functions of arbitrary
orders.
