A NOTE ON A STRUCTURE THEOREM FOR PREHOMOGENEOUS VECTOR SPACES

被引：0

作者：

Ouchi, Masaya ^{[1
,2
]}

机构：

[1] Akita Univ, Fac Educ, Akita 0108502, Japan

[2] Akita Univ, Human Studies Course, Akita 0108502, Japan

来源：

FIXED POINT THEORY | 2019年 / 20卷 / 01期

关键词：

Prehomogeneous vector space; representation theory of groups; fixed point; CLASSIFICATION;

D O I：

10.24193/fpt-ro.2019.1.18

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we give a structure theorem for all prehomogeneous vector spaces defined over the complex number field C. Also it means a necessary and sufficient condition for a triplet (G, rho, V) defined over C to be a prehomogeneous vector space. For this purpose, we give a general structural correspondence between isotropy subgroups and fixed point sets when a group acts on a non-empty set.

引用

页码：271 / 287

页数：17

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