A classification theory of prehomogeneous vector spaces. (English) Zbl 0704.20040
Representations of Lie groups: analysis on homogeneous spaces and representations of Lie groups, Proc. Symp., Kyoto/Jap. and Hiroshima/Jap. 1986, Adv. Stud. Pure Math. 14, 223-256 (1988).
[For the entire collection see Zbl 0694.00014.]
This is a survey of a classification theory of prehomogeneous vector spaces including some unpublished results of M. Sato and the author. This paper involves classifications of irreducible P.V.’s, of simple P.V.’s, of \(\lambda\)-simple P.V.’s, of reductive P.V.’s with finitely many orbits, of certain reductive P.V.’s, of regular irreducible P.V.’s with universally transitive open orbits, of irreducible P.V.’s of characteristic \(p\geq 3\), of irreducible P.V.’s of parabolic type and their real forms. Some other related results are also stated.
This is a survey of a classification theory of prehomogeneous vector spaces including some unpublished results of M. Sato and the author. This paper involves classifications of irreducible P.V.’s, of simple P.V.’s, of \(\lambda\)-simple P.V.’s, of reductive P.V.’s with finitely many orbits, of certain reductive P.V.’s, of regular irreducible P.V.’s with universally transitive open orbits, of irreducible P.V.’s of characteristic \(p\geq 3\), of irreducible P.V.’s of parabolic type and their real forms. Some other related results are also stated.
Reviewer: Chen Zhijie
MSC:
| 20G15 | Linear algebraic groups over arbitrary fields |
| 14M17 | Homogeneous spaces and generalizations |
| 20G05 | Representation theory for linear algebraic groups |
