Formes réelles des espaces préhomogènes irréductibles de type parabolique. (Real forms of irreducible prehomogeneous vector spaces of parabolic type)
type: Item
instance of: scholarly article
title: Formes réelles des espaces préhomogènes irréductibles de type parabolique. (Real forms of irreducible prehomogeneous vector spaces of parabolic type)
zbMATH Open document ID: 0588.17007
author: Hubert Rubenthaler
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74704
review text: The main result of this paper is the determination of all real forms of a regular prehomogeneous vector space of parabolic type. Let \(V_{{\mathbb{C}}}\) be a complex finite dimensional vector space. For a complex linear algebraic subgroup \(G_{{\mathbb{C}}}\) in \(GL(V_{{\mathbb{C}}})\) we call the pair \((G_{{\mathbb{C}}},V_{{\mathbb{C}}})\) a prehomogeneous vector space if there exists a Zariski-open \(G_{{\mathbb{C}}}\)-orbit in \(V_{{\mathbb{C}}}\). The author classified all the prehomogeneous vector spaces appearing in simple complex Lie algebras and called them prehomogeneous vector spaces of commutative parabolic type in his previous work. In this paper, he has determined all the real forms of such prehomogeneous vector spaces by calculating possible real forms of the root systems. His list covers all the regular irreducible prehomogeneous vector spaces. Real forms are important when we consider the local zeta function of regular prehomogeneous vector spaces.
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 14M17
zbMATH DE Number: 3944092
zbMATH Keywords: real forms
zbMATH Keywords: regular prehomogeneous vector space of parabolic type
zbMATH Keywords: complex linear algebraic subgroup
reviewed by: Masakazu Muro
MaRDI profile type: Publication
OpenAlex ID: W2316939829
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DOI: 10.5802/AIF.1036
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 3944092