An integral formula for the solutions of Knizhnik-Zamolodchikov
(KZ) equation with values in an arbitrary irreducible representation of the
symmetric group SN is presented for integer values of the parameter. The corresponding
integrals can be computed effectively as certain iterated residues
determined by a given Young diagram and give polynomials with integer coefficients.
The derivation is based on Schur-Weyl duality and the results of
Matsuo on the original SU(n) KZ equation. The duality between the spaces
of solutions with parameters m and −m is discussed in relation with the intersection
pairing in the corresponding homology groups.