English

Prehomogeneous vector spaces obtained from triangle arrangements

Representation Theory 2022-10-20 v1

Abstract

In this paper, we construct a new series of prehomogeneous vector spaces from figures made up of triangles, called triangle arrangements. Our main theorem states that, under suitable assumptions, we are able to construct a prehomogeneous vector space obtained from a triangle arrangement by attaching two triangle arrangements corresponding to prehomogeneous vector spaces at a vertex. We also give examples of prehomogeneous vector spaces obtained from triangle arrangements. Many of them seem to be new.

Keywords

Cite

@article{arxiv.2210.10467,
  title  = {Prehomogeneous vector spaces obtained from triangle arrangements},
  author = {Takeyoshi Kogiso and Hideto Nakashima},
  journal= {arXiv preprint arXiv:2210.10467},
  year   = {2022}
}

Comments

33 pages

R2 v1 2026-06-28T03:59:13.668Z