  The stationary condition (Hopf equation) for the ($n$+1) point correlation
function of a passive scalar advected by turbulent flow is argued to have an
approximate $SL(n, R)$ symmetry which provides a starting point for the
perturbative treatment of less symmetric terms. The large scale anisotropy is
found to be a relevant field, in contradiction with Kolmogorov phenomenology,
but in agreement with the large scalar skewness observed in shear flows.
Exponents are not universal, yet quantitative predictions for experiments to
test the $SL(n, R)$ symmetry can be formulated in terms of the correlation
functions.
