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

The IA-automorphism group IAₙ of the free group Fₙ of rank n is a normal subgroup of the automorphism group Aut(Fₙ) of Fₙ. We study the Albanese homology of IAₙ, which is the quotient of the rational homology of IAₙ defined as the image of the map induced by the abelianization map of IAₙ on homology. The Albanese homology of IAₙ is an algebraic GL(n,Q)-representation. We determine the representation structure of the Albanese homology of IAₙ for 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 IAₙ to the outer automorphism group of Fₙ. Moreover, we identify the relation between the stable Albanese (co)homology of IAₙ and the stable cohomology of Aut(Fₙ) with certain twisted coefficients.