  We study a class of $\Z^{d}$-substitutive subshifts, including a large family
of constant-length substitutions, and homomorphisms between them, i.e., factors
modulo isomorphisms of $\Z^{d}$. We prove that any measurable factor map and
even any homomorphism associated to a matrix commuting with the expansion
matrix, induces a continuous one. We also get strong restrictions on the
normalizer group, proving that any endomorphism is invertible, the normalizer
group is virtually generated by the shift action and the quotient of the
normalizer group by the automorphisms is restricted by the digit tile of the
substitution.
