Graded induction for Specht modules

Jun Hu and Andrew Mathas

Abstract

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

AMS Subject Classification: Primary 20C08; secondary 20C30, 05E10.