Representations of symmetric groups and structures of Lie algebra

Abstract

The aim of this thesis construct structure of Free Lie Algebra L(V ) generated by nite dimensional vector space V and decompose into irreducible components of a given degree n. To splits into irreducible component, representation of GL(V ) is main tool. However, representation of symmetric groups is used to split since representations of GL(V ) and representations of symmetric group have duality, called Schur duality. After decomposing, Kra skiewicz-Weyman theory and formula using character theory are used to determine the multiplicity of irreducible component.