Generic separation for modular invariants

TL;DR

The paper introduces a set of polynomial invariants for cyclic group representations that effectively distinguish generic orbits and generate the field of rational invariants, applicable to both indecomposable and decomposable cases.

Contribution

It provides a new explicit list of polynomial invariants of degree at most 3, plus a degree p invariant, for separating orbits in modular cyclic group representations.

Findings

Invariants of degree ≤ 3 combined with a degree p invariant separate generic orbits.

The invariants generate the entire field of rational invariants.

Results apply to both indecomposable and decomposable representations.

Abstract

For modular indecomposable representations of a cyclic group $G$ of prime order $p$ we propose a list of polynomial invariants of degree $\leq 3$ that, together with a simple invariant of degree $p$, separate generic orbits and generate the field of rational invariants. A similar result is proven for decomposable representations of $G$.