Prehomogeneous vector spaces and ergodic theory II

1996/07/01 by Akihiko Yukie, Yukie, Akihiko, Roger Zierau +3
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/9607218

openalex publication_date 1996/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply M. Ratner's theorem on closures of unipotent orbits to the study of three families of prehomogeneous vector spaces. As a result, we prove analogues of the Oppenheim Conjecture for simultaneous approximation by values of certain alternating bilinear forms in an even number of variables and certain alternating trilinear forms in six and seven variables.

Related

• Prehomogeneous vector spaces and ergodic theory I
• Prehomogeneous vector spaces and ergodic theory III
• Inhomogeneous approximation for systems of linear forms with primitivity constraints
• Prehomogeneous vector spaces, Eisenstein series, and invariant theory
• A remark on the regularity of prehomogeneous vector spaces