English

Linear orbits of alternating forms on real vector spaces

Commutative Algebra 2017-12-21 v2 Representation Theory

Abstract

In this note we complete the calculation of the number of GL(Rn)GL(\mathbb R^n)-orbits on Λk(Rn)\Lambda^k(\mathbb R^n)^*, by treating the cases (n,k)=(7,4)(n,k)= (7,4) and (8,5)(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.

Keywords

Cite

@article{arxiv.1609.02184,
  title  = {Linear orbits of alternating forms on real vector spaces},
  author = {Leonid Ryvkin},
  journal= {arXiv preprint arXiv:1609.02184},
  year   = {2017}
}
R2 v1 2026-06-22T15:43:18.140Z