Free Lie algebras as modules for symmetric groups

Let r be a positive integer, F a field of odd prime characteristic p, and L the free Lie algebra of rank r over F. Consider L a module for the symmetr ic group G(r) of all permutations of a free generating set of L. The homoge neous components L-n of L are finite dimensional submodules, and L is their direct sum. For p less than or equal to r < 2p, the main results of this p aper identify the non-projective indecomposable direct summands of the L-n as Specht modules or dual Specht modules corresponding to certain partition s. For the case r = p, the multiplicities of these indecomposables in the d irect decompositions of the L-n are also determined, as are the multiplicit ies of the projective indecomposables. (Corresponding results for p = 2 hav e been obtained elsewhere.)