Decomposition of free Lie algebras into irreducible components

Let V be a representation of a finite group G. By using the trace formula for the free Lie algebra generated by V, we compute the growth of multiplicities of irreducible components in L-n(V) as n varies. We also decompose L-alpha(V-1 + ... + V-k) and L-n(V-1 x ... x V-k) into irreducible GL(V-1) X ... X GL(V-k)-modules. (C) 1997 Academic Press.