Lie Theory

Unitary Representations and Compactifications of Symmetric Spaces

AvJean-Philippe Anker,Bent Orsted

Inbunden, Engelska, 2004

Del i serien Progress in Mathematics

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Beskrivning

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 BorelJi 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.

Produktinformation

Utgivningsdatum:2004-12-15
Mått:155 x 235 x 15 mm
Vikt:476 g
Format:Inbunden
Språk:Engelska
Serie:Progress in Mathematics
Antal sidor:207
Upplaga:2005
Förlag:Birkhauser Boston Inc
ISBN:9780817635268

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Recensioner i media

"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 Poincare 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 Mathematiques Pures et Appliquees

Innehållsförteckning

to Symmetric Spaces and Their Compactifications.- Compactifications of Symmetric and Locally Symmetric Spaces.- Restrictions of Unitary Representations of Real Reductive Groups.