The stable Albanese homology of the IA-automorphism groups of free groups

The IA-automorphism group I A n IA_n of the free group F n F_n of rank n n is a normal subgroup of the automorphism group A u t ( F n ) Aut(F_n) of F n F_n . We study the Albanese homology of I A n IA_n , which is the quotient of the rational homology of I A n IA_n defined as the image of the map induced by the abelianization map of I A n IA_n on homology. The Albanese homology of I A n IA_n is an algebraic G L ( n , Q ) GL(n,\mathbb {Q}) -representation. We determine the representation structure of the Albanese homology of I A n IA_n for n n greater than or equal to three times the homological degree. We also determine the structure of the stable Albanese homology of the analogue of I A n IA_n