04594nam a22006015i 4500001001800000003000900018005001700027007001500044008004100059020003700100024002500137040002500162050001200187050001000199072001600209072002300225072001500248082001500263082001600278245015400294264004600448300004200494336002600536337002600562338003600588347002400624490004700648505018400695520192500879650002402804650003402828650003702862650002302899650001802922650010702940650009803047650012203145650010303267650010903370700008303479700007503562710003403637773002003671776003603691776003603727830004703763856003603810912001403846942000703860950004803867999001903915952005803934978-0-8176-4430-7DE-He21320181203160137.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97808176443079978-0-8176-4430-77 a10.1007/b1390762doi aISI Library, Kolkata 4aQA252.3 4aQA387 7aPBG2bicssc 7aMAT0140002bisacsh 7aPBG2thema04a512.5522304a512.48222310aLie 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,x0743-1643 ;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. 0aTopological Groups. 0aGlobal differential geometry. 0aDifferential equations, partial. 0aHarmonic analysis. 0aGroup theory.14aTopological Groups, Lie Groups.0http://scigraph.springernature.com/things/product-market-codes/M1113224aDifferential Geometry.0http://scigraph.springernature.com/things/product-market-codes/M2102224aSeveral Complex Variables and Analytic Spaces.0http://scigraph.springernature.com/things/product-market-codes/M1219824aAbstract Harmonic Analysis.0http://scigraph.springernature.com/things/product-market-codes/M1201524aGroup Theory and Generalizations.0http://scigraph.springernature.com/things/product-market-codes/M110781 aAnker, Jean-Philippe.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aOrsted, Bent.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978081767046708iPrinted edition:z9780817635268 0aProgress in Mathematics,x0743-1643 ;v22940uhttps://doi.org/10.1007/b139076 aZDB-2-SMA cEB aMathematics and Statistics (Springer-11649) c424789d424789 9275378aMAINbMAINd2017-04-01pEB930r2018-12-03yEB