  The Macdonald polynomials with prescribed symmetry are obtained from the
nonsymmetric Macdonald polynomials via the operations of $t$-symmetrisation,
$t$-antisymmetrisation and normalisation. Motivated by corresponding results in
Jack polynomial theory we proceed to derive an expansion formula and a related
normalisation. Eigenoperator methods are used to relate the symmetric and
antisymmetric Macdonald polynomials, and we discuss how these methods can be
extended to special classes of the prescribed symmetry polynomials in terms of
their symmetric counterpart. We compute the explicit form of the normalisation
with respect to the constant term inner product. Surpassing our original
motivation, this is used to provide a derivation of a special case of a
conjectured $q$-constant term identity.
