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

Published online by Cambridge University Press:  12 March 2019

STEVEN V SAM
Affiliation:
Department of Mathematics, University of California, San Diego, CA, USA; ssam@ucsd.edu; http://math.ucsd.edu/∼ssam/
ANDREW SNOWDEN
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI, USA; asnowden@umich.edu; http://www-personal.umich.edu/∼asnowden/
Corresponding

Abstract

Twisted commutative algebras (tca’s) have played an important role in the nascent field of representation stability. Let $A_{d}$ be the 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 $\mathbf{FI}$ -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.

Type
Research Article
Creative Commons
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (http://creativecommons.org/licenses/by-nc-sa/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use.
Copyright
© The Author(s) 2019

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