  The graded Specht module $S^\lambda$ for a cyclotomic Hecke algebra comes
with a distinguished generating vector $z^\lambda\in S^\lambda$, which can be
thought of as a "highest weight vector of weight $\lambda$". This paper
describes the {\em defining relations} for the Specht module $S^\lambda$ as a
graded module generated by $z^\lambda$. The first three relations say precisely
what it means for $z^\lambda$ to be a highest weight vector of weight
$\lambda$. The remaining relations are homogeneous analogues of the classical
{\em Garnir relations}. The homogeneous Garnir relations, which are {\em
simpler} than the classical ones, are associated with a remarkable family of
homogeneous operators on the Specht module which satisfy the braid relations.
