The Image of Functor Morphing

TL;DR

This paper introduces a criterion for identifying when a representation arises from functor morphing, using parabolic subgroup actions, with applications to Borel groups over finite fields.

Contribution

It provides an explicit criterion for functor morphing representations and demonstrates its application to Borel groups of finite fields.

Findings

Established a criterion for functor morphing representations.

Applied the criterion to Borel groups over finite fields.

Enhanced understanding of automorphism group representations in finite modules.

Abstract

Functor morphing provides a method to translate complex representations of automorphism groups of finite modules over finite rings to representations of automorphism groups of functors in some abelian category. In this paper we give an explicit criterion for a representation to be in the image of functor morphing using the action of parabolic subgroups. We then demonstrate this criterion on Borel groups of finite fields.