03897nam a22005535i 4500001001800000003000900018005001700027007001500044008004100059020001800100024002500118050001200143050001000155072001600165072002300181072002300204082001500227082001600242245015400258264004600412300004200458336002600500337002600526338003600552347002400588490003500612505018400647520192500831650001702756650001802773650002402791650001602815650002302831650003602854650002702890650001702917650003602934650002702970650005102997650003203048650003803080700003503118700002703153710003403180773002003214776003603234830003503270856003803305978-0-8176-4430-7DE-He21320180115171431.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97808176443077 a10.1007/b1390762doi 4aQA252.3 4aQA387 7aPBG2bicssc 7aMAT0140002bisacsh 7aMAT0380002bisacsh04a512.5522304a512.48222310aLie Theoryh[electronic resource] :bUnitary Representations and Compactifications of Symmetric Spaces /cedited by Jean-Philippe Anker, Bent Orsted. 1aBoston, MA :bBirkhäuser Boston,c2005. aX, 207 p. 20 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aProgress in Mathematics ;v2290 ato Symmetric Spaces and Their Compactifications -- Compactifications of Symmetric and Locally Symmetric Spaces -- Restrictions of Unitary Representations of Real Reductive Groups. aSemisimple 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 with semisimple Lie groups and symmetric spaces is required of the reader. 0aMathematics. 0aGroup theory. 0aTopological groups. 0aLie groups. 0aHarmonic analysis. 0aFunctions of complex variables. 0aDifferential geometry.14aMathematics.24aTopological Groups, Lie Groups.24aDifferential Geometry.24aSeveral Complex Variables and Analytic Spaces.24aAbstract Harmonic Analysis.24aGroup Theory and Generalizations.1 aAnker, Jean-Philippe.eeditor.1 aOrsted, Bent.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817635268 0aProgress in Mathematics ;v22940uhttp://dx.doi.org/10.1007/b139076