Orthogonal roots, quadratic forms and orbits of simple graded Lie algebras
type: Item
instance of: scholarly article
title: Orthogonal roots, quadratic forms and orbits of simple graded Lie algebras
zbMATH Open document ID: 1035.17041
author: Iris Muller
published in: Journal of Algebra
publication date: 2003-04-15T00:00:00Z
review text: The purpose of this work is the study of local zeta-functions associated with regular irreducible prehomogeneous vector spaces of parabolic type. The author describes the decomposition of orbits of the prehomogeneous vector spaces in a unified way. The description of the classification of the orbits is given with the aid of classes of quadratic forms on root systems, Weyl group actions and invariants of prehomogeneous vector spaces. Her result is a generalization of a classification of quadratic forms, which was announced in the previous paper [Proc. Japan Acad., Ser. A 72, 104--107 (1996; Zbl 0860.17009)]. She also considers a prehomogeneous vector space whose parabolic group action is again prehomogeneous. The theory of zeta-functions will be developed in a future paper.
reviewed by: Masakazu Muro
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 11S90
Mathematics Subject Classification ID: 11M38
zbMATH DE Number: 1762101
zbMATH Keywords: local zeta-functions
zbMATH Keywords: prehomogeneous vector spaces of parabolic type
MaRDI profile type: Publication
full work available at URL: jabr.2002.9078
OpenAlex ID: W2023547842
Wikidata QID: Q115395652
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DOI: 10.1006/JABR.2002.9078
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description: scientific article; zbMATH DE number 1762101