Graded induction for Specht modules

Abstract

Recently Brundan, Kleshchev and Wang introduced a $\mathbb{Z}$-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.

19 pages, latex