Universal Specht modules for cyclotomic Hecke algebras

Details Universal Specht modules for cyclotomic Hecke algebras Universal Specht modules for cyclotomic Hecke algebras

2011-02-17

arxiv.org/abs/1102.3519v1

Mathematics

Representation Theory

44 pages. Extensive use of PGF/tikz to draw braid diagrams

Scientific paper

The graded Specht module $S^\lambda$ for a cyclotomic Hecke algebra comes with a distinguished generating vector $z^\lambda\in S^\lambda$, which can be thought of as a "highest weight vector of weight $\lambda$". This paper describes the {\em 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 {\em Garnir relations}. The homogeneous Garnir relations, which are {\em simpler} than the classical ones, are associated with a remarkable family of homogeneous operators on the Specht module which satisfy the braid relations.

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