  Twisted commutative algebras (tca's) have played an important role in the
nascent field of representation stability. Let A_d be the complex tca freely
generated by d indeterminates of degree 1. In a previous paper, we determined
the structure of the category of A_1-modules (which is equivalent to the
category of FI-modules). In this paper, we establish analogous results for the
category of A_d-modules, for any d. Modules over A_d are closely related to the
structures used by the authors in previous works studying syzygies of Segre and
Veronese embeddings, and we hope the results of this paper will eventually lead
to improvements on those works. Our results also have implications in
asymptotic commutative algebra.
