Lie Theory - Unitary Representations and Compactifications of Symmetric Spaces (Hardcover, 2005 ed.)

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 Borela "Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Borela "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 Harisha "Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization areintroduced. Concrete examples and relevant exercises engage the reader.

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

General

Imprint:	Birkhauser Boston
Country of origin:	United States
Series:	Progress in Mathematics, 229
Release date:	December 2004
First published:	2005
Editors:	Jean-Philippe Anker • Bent Orsted
Dimensions:	235 x 155 x 14mm (L x W x T)
Format:	Hardcover
Pages:	207
Edition:	2005 ed.
ISBN-13:	978-0-8176-3526-8
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General
LSN:	0-8176-3526-2
Barcode:	9780817635268

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