GL-EQUIVARIANT MODULES OVER POLYNOMIAL RINGS IN INFINITELY MANY VARIABLES. II

Abstract

Twisted commutative algebras (tca’s) have played an important role in the nascent field of representation stability. Let Ad be the tca freely generated by d indeterminates of degree 1. In a previous paper, we determined the structure of the category of A1-modules (which is equivalent to the category of FI-modules). In this paper, we establish analogous results for the category of Ad-modules, for any d. Modules over Ad 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.