Decomposition of Free Lie Algebras into Irreducible Components Original Research Article

LetVbe a representation of a finite groupG. By using the trace formula for the free Lie algebra generated byV, we compute the growth of multiplicities of irreducible components in imagen(V) asnvaries. We also decompose imageα(V1 circled plus ··· circled plus Vk) and imagen(V1 circle times operator ··· circle times operator Vk) into irreducibleGL(V1) × ··· × GL(Vk)-modules.