Deligne categories and representations of the finite general linear group, part 1: universal property

Inna Entova Aizenbud, Thorsten Heidersdorf

Research output: Working paperPreprint

Abstract

We study the Deligne interpolation categories Rep––––(GLt(Fq)) for t∈C, first introduced by F. Knop. These categories interpolate the categories of finite dimensional complex representations of the finite general linear group GLn(Fq). We describe the morphism spaces in this category via generators and relations. We show that the generating object of this category (an analogue of the representation CFnq of GLn(Fq)) carries the structure of a Frobenius algebra with a compatible Fq-linear structure; we call such objects Fq-linear Frobenius spaces, and show that Rep––––(GLt(Fq)) is the universal symmetric monoidal category generated by such an Fq-linear Frobenius space of categorical dimension t. In the second part of the paper, we prove a similar universal property for a category of representations of GL∞(Fq).
Original languageAmerican English
PublisherSpringer
Number of pages47
StateAccepted/In press - 2024

Publication series

NameTransformation Groups

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