Stable homology of automorphism groups of free groups and functor homology (II)

In the following statement, gr denotes the category of free groups of finite rank, VecQ the category of Q-vector spaces, a : gr→ VecQ the composition of abelianisation and rationalisation (a(G) = Gab ⊗ Q) and Λ the j-th exterior power. As usual, Fr is a free group of rank r; gr-Mod is the category of functors from gr to VecQ. Theorem 1. Let F : gr → VecQ be a polynomial functor of degree d and n, r non-negative integers such that r ≥ 2(n + d) + 3. Then there is a natural isomorphism