  We examine the commuting elements $\theta_i=\sum_{j\neq i}
\frac{s_{ij}}{z_i-z_j}$, $z_i\neq z_j$, $s_{ij}$ the transposition swapping $i$
and $j$, and we study their actions on irreducible $S_n$ representations. By
applying Schur-Weyl duality to the results of \cite{RV:QuasiKZ}, we establish a
Bethe Ansatz for these operators which yields joint eigenvectors for each
critical point of a master function. By examining the asymptotics of the
critical points, we establish a combinatorial description (up to monodromy) of
the critical points and show that, generically, the Bethe vectors span the
irreducible $S_n$ representations.
