Tables of prehomogeneous modules and \'etale modules of reductive algebraic groups

TL;DR

This paper compiles comprehensive tables classifying prehomogeneous and étale modules for reductive algebraic groups, serving as a valuable reference for researchers in the field.

Contribution

It provides the first complete, organized tables of prehomogeneous modules and étale modules for reductive algebraic groups with up to two simple factors.

Findings

Extensive classification tables of prehomogeneous modules

Identification of étale modules within the classification

Serves as a reference resource for algebraic group modules

Abstract

This document contains tables with the classification of prehomogeneous modules for reductive algebraic groups with up to two simple factors due to Sato, Kimura and many others, as well as corresponding tables of the \'etale modules appearing in this list, determined by the author. It is intended as a convenient reference for examples of \'etale module for reductive algebraic group.