  Recently Brundan, Kleshchev and Wang introduced a $\Z$-grading on the Specht
modules of the degenerate and non-degenerate cyclotomic Hecke algebras of type
$G(\ell,1,n)$. In this paper we show that induced Specht modules have an
explicit filtration by shifts of graded Specht modules. This proves a
conjecture of Brundan, Kleshchev and Wang.
