## Graded induction for Specht modules

### Jun Hu and Andrew Mathas

#### Abstract

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

Keywords: Cyclotomic Hecke algebras, Khovanov-Lauda-Rouquier algebras, cellular algebras.

: Primary 20C08; secondary 20C30, 05E10.

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 Wednesday, July 28, 2010