Universal graded Specht modules for cyclotomic Hecke algebras

The graded Specht module S-lambda for a cyclotomic Hecke algebra comes with a distinguished generating vector z(lambda)is an element of S-lambda, which can be thought of as a 'highest weight vector of weight lambda'. This paper describes the defining relations for the Specht module S-lambda as a graded module generated by z(lambda). The first three relations say precisely what it means for z(lambda) to be a highest weight vector of weight lambda. 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.