Subrepresentations in the Polynomial Representation of the Double Affine   Hecke Algebra of type $GL_n$ at $t^{k+1}q^{r-1}=1$
  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}. 
Masahiro Kasatani