Orthogonal roots, quadratic forms and orbits of simple graded Lie algebras
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.
prehomogeneous vector spaces of parabolic type
scientific article; zbMATH DE number 1762101
scientific article