LEADER 07160nam 22017655 450 001 9910154742103321 005 20190708092533.0 010 $a1-4008-8238-9 024 7 $a10.1515/9781400882380 035 $a(CKB)3710000000631402 035 $a(SSID)ssj0001651351 035 $a(PQKBManifestationID)16426211 035 $a(PQKBTitleCode)TC0001651351 035 $a(PQKBWorkID)14561379 035 $a(PQKB)10256548 035 $a(MiAaPQ)EBC4738713 035 $a(DE-B1597)467968 035 $a(OCoLC)979970578 035 $a(DE-B1597)9781400882380 035 $a(EXLCZ)993710000000631402 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aUnitary Representations of Reductive Lie Groups. (AM-118), Volume 118 /$fDavid A. Vogan 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$dİ1988 215 $a1 online resource (320 pages) 225 0 $aAnnals of Mathematics Studies ;$v349 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-691-08481-5 311 $a0-691-08482-3 320 $aBibliography. 327 $tFrontmatter -- $tCONTENTS -- $tACKNOWLEDGEMENTS -- $tINTRODUCTION -- $tChapter 1. COMPACT GROUPS AND THE BOREL-WEIL THEOREM -- $tChapter 2. HARISH-CHANDRA MODULES -- $tChapter 3. PARABOLIC INDUCTION -- $tChapter 4. STEIN COMPLEMENTARY SERIES AND THE UNITARY DUAL OF GL(n,?) -- $tChapter 5. COHOMOLOGICAL PARABOLIC INDUCTION: ANALYTIC THEORY -- $tChapter 6. COHOMOLOGICAL PARABOLIC INDUCTION: ALGEBRAIC THEORY -- $tInterlude. THE IDEA OF UNIPOTENT REPRESENTATIONS -- $tChapter 7. FINITE GROUPS AND UNIPOTENT REPRESENTATIONS -- $tChapter 8. LANGLANDS' PRINCIPLE OF FUNCTORIALITY AND UNIPOTENT REPRESENTATIONS -- $tChapter 9. PRIMITIVE IDEALS AND UNIPOTENT REPRESENTATIONS -- $tChapter 10. THE ORBIT METHOD AND UNIPOTENT REPRESENTATIONS -- $tChapter 11. E-MULTIPLICITIES AND UNIPOTENT REPRESENTATIONS -- $tChapter 12. ON THE DEFINITION OF UNIPOTENT REPRESENTATIONS -- $tChapter 13. EXHAUSTION -- $tREFERENCES -- $tBackmatter 330 $aThis book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations. 410 0$aAnnals of mathematics studies ;$vno. 118. 606 $aLie groups 606 $aRepresentations of Lie groups 610 $aAbelian group. 610 $aAdjoint representation. 610 $aAnnihilator (ring theory). 610 $aAtiyah?Singer index theorem. 610 $aAutomorphic form. 610 $aAutomorphism. 610 $aCartan subgroup. 610 $aCircle group. 610 $aClass function (algebra). 610 $aClassification theorem. 610 $aCohomology. 610 $aCommutator subgroup. 610 $aComplete metric space. 610 $aComplex manifold. 610 $aConjugacy class. 610 $aCotangent space. 610 $aDimension (vector space). 610 $aDiscrete series representation. 610 $aDixmier conjecture. 610 $aDolbeault cohomology. 610 $aDuality (mathematics). 610 $aEigenvalues and eigenvectors. 610 $aExponential map (Lie theory). 610 $aExponential map (Riemannian geometry). 610 $aExterior algebra. 610 $aFunction space. 610 $aGroup homomorphism. 610 $aHarmonic analysis. 610 $aHecke algebra. 610 $aHilbert space. 610 $aHodge theory. 610 $aHolomorphic function. 610 $aHolomorphic vector bundle. 610 $aHomogeneous space. 610 $aHomomorphism. 610 $aInduced representation. 610 $aInfinitesimal character. 610 $aInner automorphism. 610 $aInvariant subspace. 610 $aIrreducibility (mathematics). 610 $aIrreducible representation. 610 $aIsometry group. 610 $aIsometry. 610 $aK-finite. 610 $aKazhdan?Lusztig polynomial. 610 $aLanglands decomposition. 610 $aLie algebra cohomology. 610 $aLie algebra representation. 610 $aLie algebra. 610 $aLie group action. 610 $aLie group. 610 $aMathematical induction. 610 $aMaximal compact subgroup. 610 $aMeasure (mathematics). 610 $aMinkowski space. 610 $aNilpotent group. 610 $aOrbit method. 610 $aOrthogonal group. 610 $aParabolic induction. 610 $aPrincipal homogeneous space. 610 $aPrincipal series representation. 610 $aProjective space. 610 $aPseudo-Riemannian manifold. 610 $aPullback (category theory). 610 $aRamanujan?Petersson conjecture. 610 $aReductive group. 610 $aRegularity theorem. 610 $aRepresentation of a Lie group. 610 $aRepresentation theorem. 610 $aRepresentation theory. 610 $aRiemann sphere. 610 $aRiemannian manifold. 610 $aSchwartz space. 610 $aSemisimple Lie algebra. 610 $aSheaf (mathematics). 610 $aSign (mathematics). 610 $aSpecial case. 610 $aSpectral theory. 610 $aSub"ient. 610 $aSubgroup. 610 $aSupport (mathematics). 610 $aSymplectic geometry. 610 $aSymplectic group. 610 $aSymplectic vector space. 610 $aTangent space. 610 $aTautological bundle. 610 $aTheorem. 610 $aTopological group. 610 $aTopological space. 610 $aTrivial representation. 610 $aUnitary group. 610 $aUnitary matrix. 610 $aUnitary representation. 610 $aUniversal enveloping algebra. 610 $aVector bundle. 610 $aWeyl algebra. 610 $aWeyl character formula. 610 $aWeyl group. 610 $aZariski's main theorem. 610 $aZonal spherical function. 615 0$aLie groups. 615 0$aRepresentations of Lie groups. 676 $a512/.55 700 $aVogan$b David A., $049960 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154742103321 996 $aUnitary Representations of Reductive Lie Groups. (AM-118), Volume 118$92788876 997 $aUNINA