Invariant theory of finite general linear groups modulo Frobenius powers

ABSTRACT

We prove some cases of a conjecture of Lewis, Reiner and Stanton regarding Hilbert series corresponding to the action of $G{l}_n\left({𝔽}_q\right)$ 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.

KEYWORDS:

• Frobenius powers
• general linear groups
• invariant theory

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 13A50