Overview
- 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
Part of the book series: Progress in Mathematics (PM, volume 229)
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Table of contents(3 chapters)
Keywords
About this book
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, i.e. restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles.
Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples and provides a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Kobayashi examines the important subject of branching laws.
Knowledge of basic representation theory of Lie groups and familiarity with semisimple Lie groups and symmetric spaces is required of the reader.Reviews
Editors and Affiliations
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Laboratoire de Mathématiques (MAPMO), Université d’Orléans, Orléans Cedex 2, France
Jean-Philippe Anker
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Department of Mathematics and Computer Science, University of Southern Denmark, Odense M, Denmark
Bent Orsted
Bibliographic Information
Book Title: Lie Theory
Book Subtitle: Unitary Representations and Compactifications of Symmetric Spaces
Editors: Jean-Philippe Anker, Bent Orsted
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/b139076
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2005
Hardcover ISBN: 978-0-8176-3526-8
eBook ISBN: 978-0-8176-4430-7
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: X, 207
Number of Illustrations: 20 b/w illustrations
Topics: Topological Groups, Lie Groups, Differential Geometry, Several Complex Variables and Analytic Spaces, Abstract Harmonic Analysis, Group Theory and Generalizations