On parameterizations of rational orbits of some forms of prehomogeneous vector spaces

Abstract

In this paper, we consider the structure of rational orbit of some prehomogeneous vector spaces originally motivated by Wright and Yukie. After we give a refinement of Wright-Yukie's construction, we apply it to the inner forms of the $D_5$ and $E_7$ types. Parameterizations of reducible algebras for the cubic cases are included.

16pages

References in corpus (2)

• Distributions of discriminants of cubic algebras
• A remark on the regularity of prehomogeneous vector spaces