Manfred Schocker:

Embeddings of Higher Lie Modules

The higher Lie modules of the general linear group GL(V) over a finite dimensional vector space V arise naturally from the Poincaré-Birkhoff-Witt basis of the tensor algebra over V. They are indexed by partitions. For the higher Lie modules corresponding to hook partitions of n a complete chain of embeddings is obtained. As an application, a new inductive proof of Klyachko's result on the irreducible components of the classical Lie module is given. Additionally, all irreducible components of multiplicity 1 are determined.

Mathematics Subject Classification (1991): 20G05, 17B01, 20C30

Bibliographical note: angenommen bei J. Pure Appl. Alg

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[Thu Feb 19 18:56:35 2009]

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