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http://hdl.handle.net/20.500.12358/24119
TitleParametrization of the orbits of the real forms SU (p, q) and SO(p, q) in Grassmannian
Untitled
Abstract

Let G  be a complex semi-simple Lie group with real form G0. Let Z = G/P be identified with Gr(k, n), the Grassmannian of k planes in Cn. Equivalently, P is a maximal  parabolic subgroup defined by the dimension sequence (k, n − k). Consider the action of G0  on the Grassmannian Gr(k, n). It is known that G0 has only finitely many orbits in G/P and therefore it has a unique closed orbit and at least one open orbit ([2],[6]). In this paper we will prove that the G0-orbits in Gr(k, n) are parameterized by signature, where G0 is SU (p, q) and SO(p, q) a real form of SL(n, C) and SO(p, q) respectively .

Authors
Abu-Shoga, Faten S.
TypeJournal Article
Date2018
LanguageEnglish
Subjects
non-degenerate subspace
grassmannian
orbit
degenerate subspace
isotropic
Published inIUG Journal of Natural Studies
SeriesVolume: 26, Number: 2
Publisherالجامعة الإسلامية - غزة
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  • Staff Publications- Faculty of Science [910]
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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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