Adequate subgroups
Robert Guralnick, Florian Herzig, Richard Taylor, Jack Thorne
TL;DR
This paper investigates the properties of adequate subgroups within the general linear group over finite fields, providing criteria that help in understanding their role in automorphy lifting theorems.
Contribution
It offers a new sufficient condition for subgroups to be considered adequate, advancing the theoretical framework in this area.
Findings
Established a criterion for adequacy of subgroups
Enhanced understanding of subgroup structures in automorphy lifting
Provided tools for future research in automorphic forms
Abstract
We study adequate subgroups of over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a subgroup to be adequate.
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