Lie Theory : Unitary Representations and Compactifications of Symmetric Spaces

Jean-Philippe Anker

ISBN 10: 0817635262 / ISBN 13: 9780817635268

Verlag: Birkhauser Boston Dez 2004, 2004

Beschreibung

Neuware - Focuses on two fundamental questions related to semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications, and branching laws for unitary representationsWide applications of compactification techniquesConcrete examples and relevant exercises engage the reader Knowledge of basic representation theory of Lie groups, semisimple Lie groups and symmetric spaces is required.

Bestandsnummer des Verkäufers 9780817635268

Bibliografische Details

• Titel: Lie Theory : Unitary Representations and Compactifications of Symmetric Spaces
• Verlag: Birkhauser Boston Dez 2004
• Erscheinungsjahr: 2004
• Sprache: Englisch
• ISBN-10: 0817635262
• ISBN-13: 9780817635268
• Einband: Buch
• Zustand: Neu
• Abmessungen: 240B x 161 H x 15 T Millimeter Breite: 240 mm, Höhe: 161 mm, Tiefe: 15 mm
• Gewicht: 476 Gramm

Über diesen Titel

Inhaltsangabe

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.

Von der hinteren Coverseite

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, 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. A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide 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. Borel–Ji further examine constructions of Oshima, De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques.

Kobayashi examines the important subject of branching laws. Important concepts from modern representation theory, such as Harish–Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization are introduced. Concrete examples and relevant exercises engage the reader.

Knowledge of basic representation theory of Lie groups as well as familiarity withsemisimple Lie groups and symmetric spaces is required of the reader.