Jordan theoretic G-orbits and flag varieties

Jordan theoretic G-orbits and flag varieties

The Jordan theoretic approach to bounded symmetric domains G/K is used to determine the G-orbits on the compact dual of G/K as well as their Matsuki-duals in an explicit way. For this we use a generalized version of the Peirce decomposition within Jordan triple systems and the notion of pseudo-inver...

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Bibliographic Details
Main Author: Schwarz, Benjamin
Contributors: Upmeier, Harald (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Language:English
Published: Philipps-Universität Marburg 2010
Subjects:
Mathematik
Halbeinfache Lie-Gruppe
Determinantenfunktionen
Fahnenmannigfaltigkeit
Jordantheorie
Hermitescher symmetrischer Raum
Orbit <Mathematik>
Jordan theory
Determinant functions
Mathematics
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Summary:The Jordan theoretic approach to bounded symmetric domains G/K is used to determine the G-orbits on the compact dual of G/K as well as their Matsuki-duals in an explicit way. For this we use a generalized version of the Peirce decomposition within Jordan triple systems and the notion of pseudo-inverses. As a second result of this thesis we develope a Jordan theoretic model for generalized flag varieties and use this to give a Jordan theoretic description of the so called determinant functions introduced by L. Barchini, S.G. Gindikin and H.W. Wong.
DOI:10.17192/z2010.0625

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