# Invariant Theory of finite general linear groups modulo Frobenius powers

## TL;DR

This paper investigates the invariant theory of finite general linear groups acting on polynomial rings modulo Frobenius powers, proving some cases of a conjecture and proposing new conjectures for further study.

## Contribution

It proves specific cases of a conjecture relating to Hilbert series of invariants under group action and introduces new conjectures about invariant rings.

## Key findings

- Proved certain cases of the Lewis-Reiner-Stanton conjecture.
- Provided new conjectures on invariant rings for specific cases.
- Advanced understanding of invariants under finite linear group actions.

## Abstract

We prove some cases of a conjecture of Lewis, Reiner and Stanton regarding Hilbert series corresponding to the action of $Gl_n(\mathbb{F}_q)$ on a polynomial ring modulo Frobenius powers. We also give a few conjectures about the invariant ring for certain cases that we don't prove completely.