Graded Induction for Specht Modules

Brundan, Kleshchev, and Wang have introduced a $\mathbb Z$-grading on the Specht modules of the degenerate and nondegenerate cyclotomic Hecke algebras of type G(ℓ,1,n). In this paper, we show that the induced Specht modules have an explicit filtration by shifts of graded Specht modules. This proves a conjecture of Brundan, Kleshchev, and Wang. To prove these results, we first establish several strong results about the transition matrices between the seminormal, standard, and homogeneous bases of these algebras and similar results for the action of the Jucys–Murphy elements on these bases.