  We prove that the quotient of the polynomial representation of the double
affine Hecke algebra (DAHA) by the radical of the duality pairing is always
irreducible assuming that it is finite dimensional (apart from the roots of
unity). We also find necessary and sufficient conditions for the radical to be
zero, which is a q-generalization of Opdam's formula for the singular
k-parameters with the multiple zero-eigenvalues of the corresponding Dunkl
operators.
