Linear orbits of alternating forms on real vector spaces

Abstract

In this note we complete the calculation of the number of $GL({\mathbb{R}}^n)$-orbits on ${\Lambda }^k({\mathbb{R}}^n{)}^{\ast }$, by treating the cases $(n,k)=(7,4)$ and $(8,5)$ not covered in the literature. We also calculate the number of of non-degenerate and stable orbits, as they are of special interest to multisymplectic and special geometry.

Cited by in corpus (2)

• An invitation to multisymplectic geometry
• Classification of $k$-forms on ${\mathbf{R}}^n$ and the existence of associated geometry on manifolds