  We study a Laurent polynomial representation $V$ of the double affine Hecke
algebra of type $GL_n$ for specialized parameters
  $t^{k+1}q^{r-1}=1$. We define a series of subrepresentations of $V$ by using
a vanishing condition. For some cases, we give an explicit basis of the
subrepresentation in terms of nonsymmetric Macdonald polynomials. These results
are nonsymmetric versions of \cite{FJMM} and \cite{KMSV}.
