Prehomogeneous tensor spaces

TL;DR

This paper refines the classification of prehomogeneous tensor spaces, offering a quick method to determine whether a given tensor space is prehomogeneous, building on the foundational work of Sato-Kimura.

Contribution

It introduces a streamlined approach for identifying prehomogeneous tensor spaces, enhancing the existing classification framework.

Findings

Provides a quick check method for prehomogeneity in tensor spaces

Refines the classification of prehomogeneous vector spaces in tensor cases

Builds on Sato-Kimura's foundational classification

Abstract

We refine the classification of prehomogeneous vector spaces, provided by Sato-Kimura, in the case of tensor spaces, presenting a quick way to check whether a given tensor space is prehomogeneous or not.