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Generic separation for modular invariants

Fabian Reimers, Müfit Sezer

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 $G$.

Generic separation for modular invariants

Abstract

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

Paper Structure

This paper contains 6 sections, 12 theorems, 32 equations.

Table of Contents

  1. Introduction
  2. Basics about generically separating invariants
  3. Cyclic group of prime order
  4. Degree two connecting invariant
  5. Degree three connecting invariants
  6. Main results

Key Result

Proposition 1

Consider the following properties for a list of polynomial invariants $f_1 ,\ldots , f_r \in \Bbbk[V]^G$: Then (1) and (2) are equivalent, and, if $\Bbbk$ is infinite, (1) implies (3).

Theorems & Definitions (29)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Proposition 3
  • proof
  • ...and 19 more