Universal graded Specht modules for cyclotomic Hecke algebras

Abstract

The graded Specht module S for a cyclotomic Hecke algebra comes with a distinguished generating vector z∈S, which can be thought of as a 'highest weight vector of weight. This paper describes the defining relations for the Specht module S as a graded module generated by z. The first three relations say precisely what it means for z to be a highest weight vector of weight . The remaining relations are homogeneous analogues of the classical Garnir relations. The homogeneous Garnir relations, which are simpler than the classical ones, are associated with a remarkable family of homogeneous operators on the Specht module which satisfy the braid relations. © 2012 London Mathematical Society.