04350nam 2200661Ia 450 991077749610332120221107222739.01-281-92488-19786611924881981-277-362-2(CKB)1000000000412229(DLC)2006283979(StDuBDS)AH24684454(SSID)ssj0000107980(PQKBManifestationID)11141609(PQKBTitleCode)TC0000107980(PQKBWorkID)10016099(PQKB)10906092(MiAaPQ)EBC1681511(WSP)00006104(Au-PeEL)EBL1681511(CaPaEBR)ebr10201453(CaONFJC)MIL192488(OCoLC)820942698(PPN)16803638X(EXLCZ)99100000000041222920060825d2006 uy 0engur|||||||||||txtccrAutomorphic representations of low rank groups[electronic resource] /Yuval Z. FlickerHackensack, N.J. World Scientificc20061 online resource (xi, 485 p.) Bibliographic Level Mode of Issuance: Monograph981-256-803-4 Includes bibliographical references and index.Preface -- pt. 1. On the symmetric square lifting introduction. 1. Functoriality and norms. 1.1. Hecke algebra. 1.2. Norms. 1.3. Local lifting. 1.4. Orthogonality. II. Orbital integrals. II.1. Fundamental lemma. II.2. Differential forms. II.3. Matching orbital integrals. II.4. Germ expansion. III. Twisted trace formula. III.1. Geometric side. III.2. Analytic side. III.3. Trace formulae. IV. Total global comparison. IV. Total global comparison. IV.1. The comparison. IV.2. Appendix: Mathematica program. V. Applications of a trace formula. V.1. Approximation. V.2. Main theorems. V.3. Characters and genericity. VI. Computation of a twisted character. VI.1. Proof of theorem, anisotropic case. VI.2. Proof of theorem, isotropic case -- pt. 2. Automorphic representations of the unitary group U(3,E/F) introduction. 1. Functorial overview. 2. Statement of results. I. Local theory. I.1. Conjugacy classes. I.2. Orbital integrals. I.3. Fundamental lemma. I.4. Admissible representations. I.5. Representations of U(2,1;C/R). 1.6. Fundamental lemma again. II. Trace formula. II.1. Stable trace formula. II.2. Twisted trace formula. II.3. Restricted comparison. II.4. Trace identity. II.5. The [symbol]-endo-lifting e'. II.6. The quasi-endo-lifting e. II.7. Unitary symmetric square. III. Liftings and packets. III.1. Local identity. III.2. Separation. III.3. Specific lifts. III.4. Whittaker models and twisted characters. III.5. Global lifting. III.6. Concluding remarks -- pt. 3. Zeta functions of Shimura varieties of U(3) introduction. 1. Statement of results. 2. The zeta function. I. Preliminaries. I.1. The Shumira variety. I.2. Decomposition of cohomology. I.3. Galois representations. II. Automorphic representations. II.1. Stabilization and the test function. II.2. Functorial overview of basechange for U(3). II.3. Local results on basechange for U(3). II.4. Global results on basechange for U(3). II.5. Spectral side of the stable trace formula. II.6. Proper endoscopic group. III. Local terms. III.1. The reflex field. III.2. The representation of the dual group. III.3. Local terms at p. III.4. The eigenvalues at p. III.5. Terms at p for the endoscopic group. IV. Real representations. IV.1. Representations of the real GL(2). IV.2. Representations of U(2,l). IV.3. Finite-dimensional representations. V. Galois representations. V.1. Stable case. V.2. Unstable case. V.3. Nontempered case.Representations of groupsUnitary groupsLifting theoryAutomorphic formsTrace formulasRepresentations of groups.Unitary groups.Lifting theory.Automorphic forms.Trace formulas.512.22Flicker Yuval Z(Yuval Zvi),1955-1501799MiAaPQMiAaPQMiAaPQBOOK9910777496103321Automorphic representations of low rank groups3829386UNINA