A remark on the regularity of prehomogeneous vector spaces

1997/08/28 by Yukie, Akihiko
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/9708209

Abstract

In this note, we prove that if (G,V) is a prehomogeneous vector space over any field k such that the stabilizer of a generic point is reductive, the set of semi-stable points is a single orbit over the separable closure of k.

Related

• On the GIT stratification of prehomogeneous vector spaces II
• On the GIT stratification of prehomogeneous vector spaces III
• On the GIT stratification of prehomogenous vector spaces IV
• Prehomogeneous vector spaces and ergodic theory III
• Prehomogeneous vector spaces and ergodic theory I