Ulteriori informazioni
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
Sommario
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
Riassunto
Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title
Lie Theory
, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory.
Unitary Representations and Compactifications of Symmetric Spaces
, a self-contained work by A. Borel, L. Ji, and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications, and branching laws for unitary representations. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups and symmetric spaces is required of the reader.
Testo aggiuntivo
"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 chapter...is 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
Relazione
"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 chapter...is 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
