Universal graded Specht modules for cyclotomic Hecke algebras

The graded Specht module Sλ for a cyclotomic Hecke algebra comes with a distinguished generating vector zλ∈Sλ, which can be thought of as a ‘highest weight vector of weight λ’. This paper describes the defining relations for the Specht module Sλ as a graded module generated by zλ. The first three re...

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Bibliographic Details
Published in:Proceedings of the London Mathematical Society 2012-12, Vol.105 (6), p.1245-1289
Main Authors: Kleshchev, Alexander S., Mathas, Andrew, Ram, Arun
Format: Article
Language:English
Subjects:
Algebra
Braiding
Mathematical analysis
Modules
Operators
Vectors (mathematics)
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Summary:The graded Specht module Sλ for a cyclotomic Hecke algebra comes with a distinguished generating vector zλ∈Sλ, which can be thought of as a ‘highest weight vector of weight λ’. This paper describes the defining relations for the Specht module Sλ as a graded module generated by zλ. The first three relations say precisely what it means for zλ to be a highest weight vector of weight λ. 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.
ISSN:0024-6115
1460-244X
DOI:10.1112/plms/pds019