Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces

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Dezember 2004



* Focuses on two fundamental questions related to semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications, and branching laws for unitary representations
* Wide applications of compactification techniques
* Concrete examples and relevant exercises engage the reader
* Knowledge of basic representation theory of Lie groups, semisimple Lie groups and symmetric spaces is required


* Preface * Ji: Introduction to Symmetric Spaces and Their Compactifications * Borel/Ji: Compactifications of Symmetric and Locally Symmetric Spaces * Kobayashi: Restrictions of Unitary Representations of Real Reductive Groups


"The present volume consists of three chapters, and the corresponding material is based on lectures delivered by the authors to various European Schools in Group Theory. The first chapter...includes a very nice discussion of some of the basic ideas in the theory of symmetric spaces and their compactifications, starting from the fundamental examples of the Poincaré disc and the bidisc. The third a very good and most welcome introduction to a circle of ideas in representation theory centered on branching laws. The exposition includes many concrete examples...The above presentation of the contents is certainly too short to do justice to all beautiful ideas containe din its three chapters. This book should appeal to whoever has a taste for the beauty of the idea of symmetry in mathematics. If there is anyone asking only for the specific usefulness of the techniques developed here, thn we shall answer that these techniques are extremely useful to the graduate students, as well as to other people working in differential geometry, Lie theory, representation theory, or analysis on homogeneous spaces." ---Revue Roumaine de Mathématiques Pures et Appliquées
EAN: 9780817635268
ISBN: 0817635262
Untertitel: 'Progress in Mathematics'. 2005. Auflage. Sprache: Englisch.
Erscheinungsdatum: Dezember 2004
Seitenanzahl: 207 Seiten
Format: gebunden
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