  We determine the partitions $\lambda$ for which the corresponding induced
module (or Schur module in the language of Buchsbaum et. al., [1])
$\nabla(\lambda)$ is injective in the category of polynomial modules for a
general linear group over an infinite field, equivalently which Weyl modules
are projective polynomial modules. Since the problem is essentially no more
difficult in the quantised case we address it at this level of generality.
Expressing our results in terms of the representation theory of Hecke algebras
at the parameter $q$ we determine the partitions $\lambda$ for which the
corresponding Specht module is a Young module, when $1+q\neq 0$. In the
classical case this problem was addressed by D. Hemmer, [12]. The nature of the
set of partitions appearing in our solution gives a new formulation of Carter's
condition on regular partitions. On the other hand, we note, in Remark 2.22,
that the result on irreducible Weyl modules for the quantised Schur algebra
$S_q(n,n)$, [17], Theorem 5.39, given in terms of Carter partitions, may be
also used to obtain the main result presented here.
