  In a previous paper J.-G. Luque and the author (Sem. Loth. Combin. 2011)
developed the theory of nonsymmetric Macdonald polynomials taking values in an
irreducible module of the Hecke algebra of the symmetric group
$\mathcal{S}_{N}$. The polynomials are parametrized by $\left( q,t\right) $ and
are simultaneous eigenfunctions of a commuting set of Cherednik operators,
which were studied by Baker and Forrester (IMRN 1997). In the Dunkl-Luque paper
there is a construction of a pairing between $\left( q^{-1},t^{-1}\right) $
polynomials and $\left( q,t\right) $ polynomials, and for which the Macdonald
polynomials form a biorthogonal set. The present work is a sequel with the
purpose of constructing a symmetric bilinear form for which the Macdonald
polynomials form an orthogonal basis and to determine the region of $\left(
q,t\right) $-values for which the form is positive-definite. Irreducible
representations of the Hecke algebra are characterized by partitions of $N$.
The positivity region depends only on the maximum hook-length of the Ferrers
diagram of the partition.
