Prehomogeneous vector spaces obtained from triangle arrangements

Takeyoshi Kogiso; Hideto Nakashima

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arXiv · 2210.10467

Prehomogeneous vector spaces obtained from triangle arrangements

Takeyoshi Kogiso·Hideto Nakashima

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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.

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BibTeX RIS

Takeyoshi Kogiso, Hideto Nakashima. 2022-10-19. Prehomogeneous vector spaces obtained from triangle arrangements. https://arxiv.org/abs/2210.10467

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