  For each partition $\tau$ of $N$ there are irreducible modules of the
symmetric groups $\mathcal{S}_{N}$ or the corresponding Hecke algebra
$\mathcal{H}_{N}\left( t\right) $ whose bases consist of reverse standard Young
tableaux of shape $\tau$. There are associated spaces of nonsymmetric Jack and
Macdonald polynomials taking values in these modules, respectively.The Jack
polynomials are a special case of those constructed by Griffeth for the
infinite family $G\left( n,p,N\right) $ of complex reflection groups. The
Macdonald polynomials were constructed by Luque and the author. For both the
group $\mathcal{S}_{N}$ and the Hecke algebra $\mathcal{H}_{N}\left( t\right) $
there is a commutative set of Dunkl operators. The Jack and the Macdonald
polynomials are parametrized by $\kappa$ and $\left( q,t\right) $ respectively.
For certain values of the parameters (called singular values) there are
polynomials annihilated by each Dunkl operator; these are called singular
polynomials. This paper analyzes the singular polynomials whose leading term is
$x_{1}^{m}\otimes S$, where $S$ is an arbitrary reverse standard Young tableau
of shape $\tau$. The singular values depend on properties of the edge of the
Ferrers diagram of $\tau$.
