ACTIONS OF AUTOMORPHISM GROUPS OF FREE GROUPS ON SPACES OF JACOBI DIAGRAMS. II

The automorphism group Aut(F-n) of the free group F-n acts on a space A(d)(n) of Jacobi diagrams of degree d on n oriented arcs. We study the Aut(F-n)-module structure of A(d)(n) by using two actions on the associated graded vector space of A(d)(n): an action of the general linear group GL(n,Z) and an action of the graded Lie algebra gr(IA(n)) of the IA-automorphism group IA(n) of F n associated with its lower central series. We extend the action of gr(IA(n)) to an action of the associated graded Lie algebra of the Andreadakis filtration of the endomorphism monoid of F-n. By using this action, we study the Aut(F-n)-module structure of A(d)(n). We obtain an indecomposable decomposition of A(d)(n) as Aut(F-n)-modules for n >= 2d. Moreover, we obtain the radical filtration of A(d)(n) for n >= 2d and the socle of A(3)(n).