VI-modules in nondescribing characteristic, part I

Nagpal, Rohit

doi:10.2140/ant.2019.13.2151

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VI-modules in nondescribing characteristic, part I

Rohit Nagpal

Vol. 13 (2019), No. 9, 2151–2189

DOI: 10.2140/ant.2019.13.2151

Abstract

Let VI be the category of finite dimensional $F_{q}$ -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 ${GL}_{\infty} (F_{q})$ -representations in nondescribing characteristic which is contained in Part II of this paper (VI-modules in nondescribing characteristic, part II, arxiv:1810.04592).

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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

Vol. 13, No. 9, 2019