  For each irreducible module of the symmetric group $\mathcal{S}_{N}$ there is
a set of parametrized nonsymmetric Jack polynomials in $N$ variables taking
values in the module. These polynomials are simultaneous eigenfunctions of a
commutative set of operators, self-adjoint with respect to two Hermitian forms,
one called the contravariant form and the other is with respect to a
matrix-valued measure on the $N$-torus. The latter is valid for the parameter
lying in an interval about zero which depends on the module. The author in a
previous paper [SIGMA 12 (2016), 033, 27 pages, arXiv:1511.06721] proved the
existence of the measure and that its absolutely continuous part satisfies a
system of linear differential equations. In this paper the system is analyzed
in detail. The $N$-torus is divided into $(N-1)!$ connected components by the
hyperplanes $x_{i}=x_{j}$, $i<j$, which are the singularities of the system.
The main result is that the orthogonality measure has no singular part with
respect to Haar measure, and thus is given by a matrix function times Haar
measure. This function is analytic on each of the connected components.
