  Motivated by Stanley's conjecture on the multiplication of Jack symmetric
functions, we prove a couple of identities showing that skew Jack symmetric
functions are semi-invariant up to translation and rotation of a $\pi$ angle of
the skew diagram. It follows that, in some special cases, the coefficients of
the skew Jack symmetric functions with respect to the basis of the monomial
symmetric functions are polynomials with nonnegative integer coefficients.
