  Let $n$ be a positive integer, and let $\mathscr{H}_n$ denote the affine KLR
algebra in type A. Kleshchev, Mathas and Ram have given a homogeneous
presentation for graded column Specht modules $\operatorname{S}_{\lambda}$ for
$\mathscr{H}_n$. Given two multipartitions $\lambda$ and $\mu$, we define the
notion of a \emph{dominated} homomorphism
$\operatorname{S}_{\lambda}\to\operatorname{S}_{\mu}$, and use the KMR
presentation to prove a generalised column removal theorem for graded dominated
homomorphisms between Specht modules. In the process, we prove some useful
properties of $\mathscr{H}_n$-homomorphisms between Specht modules which lead
to an immediate corollary that, subject to a few demonstrably necessary
conditions, every homomorphism
$\operatorname{S}_{\lambda}\to\operatorname{S}_{\mu}$ is dominated, and in
particular
$\operatorname{Hom}_{\mathscr{H}_n}(\operatorname{S}_{\lambda},\operatorname{S}_{\mu})=0$
unless $\lambda$ dominates $\mu$.
  Brundan and Kleshchev show that certain cyclotomic quotients of
$\mathscr{H}_n$ are isomorphic to (degenerate) cyclotomic Hecke algebras of
type A. Via this isomorphism, our results can be seen as a broad generalisation
of the column removal results of Fayers and Lyle and of Lyle and Mathas;
generalising both into arbitrary level and into the graded setting.
