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＜E-Book＞
Lie Theory : Unitary Representations and Compactifications of Symmetric Spaces / edited by Jean-Philippe Anker, Bent Orsted
(Progress in Mathematics. ISSN:2296505X ; 229)

Edition	1st ed. 2005.
Publisher	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
Year	2005
Language	English
Size	X, 207 p. 20 illus : online resource
Authors	Anker, Jean-Philippe editor Orsted, Bent editor SpringerLink (Online service)
Subjects	LCSH:Topological groups LCSH:Lie groups LCSH:Geometry, Differential LCSH:Functions of complex variables LCSH:Harmonic analysis LCSH:Group theory FREE:Topological Groups and Lie Groups FREE:Differential Geometry FREE:Several Complex Variables and Analytic Spaces FREE:Abstract Harmonic Analysis FREE:Group Theory and Generalizations
Notes	to Symmetric Spaces and Their Compactifications -- Compactifications of Symmetric and Locally Symmetric Spaces -- Restrictions of Unitary Representations of Real Reductive Groups 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 HTTP:URL=https://doi.org/10.1007/b139076

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