Lie Theory [electronic resource] : Unitary Representations and Compactifications of Symmetric Spaces / edited by JeanPhilippe Anker, Bent Orsted.
Contributor(s): Anker, JeanPhilippe [editor.]  Orsted, Bent [editor.]  SpringerLink (Online service).
Material type: TextSeries: Progress in Mathematics: 229Publisher: Boston, MA : Birkhäuser Boston, 2005Description: X, 207 p. 20 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780817644307.Subject(s): Topological Groups  Global differential geometry  Differential equations, partial  Harmonic analysis  Group theory  Topological Groups, Lie Groups  Differential Geometry  Several Complex Variables and Analytic Spaces  Abstract Harmonic Analysis  Group Theory and GeneralizationsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 512.55  512.482 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

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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, selfcontained volumes, under the general title Lie Theory, feature survey work and original results by wellestablished researchers in key areas of semisimple Lie theory. Unitary Representations and Compactifications of Symmetric Spaces, a selfcontained 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 with semisimple Lie groups and symmetric spaces is required of the reader.
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