Vol. 13, No. 9, 2019

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VI-modules in nondescribing characteristic, part I

Rohit Nagpal

Vol. 13 (2019), No. 9, 2151–2189
Abstract

Let VI be the category of finite dimensional Fq-vector spaces whose morphisms are injective linear maps and let k be a noetherian ring. We study the category of functors from VI to k-modules in the case when q is invertible in k. Our results include a structure theorem, finiteness of regularity, and a description of the Hilbert series. These results are crucial in the classification of smooth irreducible GL(Fq)-representations in nondescribing characteristic which is contained in Part II of this paper (VI-modules in nondescribing characteristic, part II, arxiv:1810.04592).

Keywords
VI-modules, FI-modules, finite general linear groups, representation stability
Mathematical Subject Classification 2010
Primary: 20C33
Secondary: 13D45, 20J05
Milestones
Received: 20 November 2018
Revised: 30 May 2019
Accepted: 22 July 2019
Published: 7 December 2019
Authors
Rohit Nagpal
Department of Mathematics
University of Chicago
IL
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States