Relations between modular invariants of a vector and a covector in dimension two

TL;DR

This paper identifies generating relations for the modular invariant ring involving a vector and a covector under the action of the two-dimensional general linear group over a finite field, advancing understanding of invariant theory in this setting.

Contribution

It provides explicit generating relations for the modular invariant ring of a vector and a covector in two dimensions, a novel result in invariant theory.

Findings

Derived explicit relations for the invariant ring

Enhanced understanding of modular invariants in two dimensions

Contributed to the theory of invariants under finite group actions

Abstract

We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.