  The affine Hecke algebra of type $A$ has two parameters $\left( q,t\right) $
and acts on polynomials in $N$ variables. There are two important pairwise
commuting sets of elements in the algebra: the Cherednik operators and the
Jucys-Murphy elements whose simultaneous eigenfunctions are the nonsymmetric
Macdonald polynomials, and basis vectors of irreducible modules of the Hecke
algebra, respectively. For certain parameter values it is possible for special
polynomials to be simultaneous eigenfunctions with equal corresponding
eigenvalues of both sets of operators. These are called singular polynomials.
The possible parameter values are of the form $q^{m}=t^{-n}$ with $2\leq n\leq
N.$ For a fixed parameter the singular polynomials span an irreducible module
of the Hecke algebra. Colmenarejo and the author (SIGMA 16 (2020), 010) showed
that there exist singular polynomials for each of these parameter values, they
coincide with specializations of nonsymmetric Macdonald polynomials, and the
isotype (a partition of $N$) of the Hecke algebra module is $\left(
dn-1,n-1,\ldots,n-1,r\right) $ for some $d\geq1$. In the present paper it is
shown that there are no other singular polynomials.
