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.
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}
}
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33 pages