Manfred Schocker

Noncommutative character theory of the symmetric group

The Inductive Method Noncommutative Character Theory of the Symmetric Group Classical Character Theory of the Symmetric Group Appendices: Elements of Representation Theory Solomons Mackey Formula Young Tableaux and Knuth Relations

Embeddings of higher Lie modules

Abstract The higher Lie modules of the general linear group GL( V ) over a finite dimensional vector space V arise naturally from the Poincare–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 Klyachkos result on the irreducible components of the classical Lie module is given. Additionally, all irreducible components of multiplicity 1 are determined.