Embedding the flag representation in divided powers

TL;DR

This paper generalizes a theorem on embedding flag representations into divided powers over any finite field, utilizing the category of functors from finite-dimensional vector spaces to vector spaces.

Contribution

It extends previous results by Crabb and Hubbuck to arbitrary finite fields using a functor category framework.

Findings

Generalized embedding theorem for flag representations in divided powers

Applicable to any finite field F

Provides a new categorical approach to the problem

Abstract

A generalization of a theorem of Crabb and Hubbuck concerning the embedding of flag representations in divided powers is given, working over an arbitrary finite field F, using the category of functors from finite-dimensional F-vector spaces to F-vector spaces.