LEADER 06032nam 2200745Ia 450 001 9910953383603321 005 20251116203732.0 010 $a9786611924881 010 $a9781281924889 010 $a1281924881 010 $a9789812773623 010 $a9812773622 035 $a(CKB)1000000000412229 035 $a(DLC)2006283979 035 $a(StDuBDS)AH24684454 035 $a(SSID)ssj0000107980 035 $a(PQKBManifestationID)11141609 035 $a(PQKBTitleCode)TC0000107980 035 $a(PQKBWorkID)10016099 035 $a(PQKB)10906092 035 $a(MiAaPQ)EBC1681511 035 $a(WSP)00006104 035 $a(Au-PeEL)EBL1681511 035 $a(CaPaEBR)ebr10201453 035 $a(CaONFJC)MIL192488 035 $a(OCoLC)820942698 035 $a(PPN)16803638X 035 $a(Perlego)849228 035 $a(BIP)13526665 035 $a(EXLCZ)991000000000412229 100 $a20060825d2006 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAutomorphic representations of low rank groups /$fYuval Z. Flicker 205 $a1st ed. 210 $aHackensack, N.J. $cWorld Scientific$dc2006 215 $a1 online resource (xi, 485 p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9789812568038 311 08$a9812568034 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThe area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings". This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), E: F] = 2.The book develops the technique of comparison of twisted and stabilized trace formulae and considers the "Fundamental Lemma" on orbital integrals of spherical functions. Comparison of trace formulae is simplified using "regular" functions and the "lifting" is stated and proved by means of character relations.This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, and a definition of packets for U(3), a proof of multiplicity one theorem and rigidity theorem for SL(2) and for U(3), a determination of the self-contragredient representations of PGL(3) and those on GL(3, E) fixed by transpose-inverse-bar. In particular, the multiplicity one theorem is new and recent.There are applications to construction of Galois representations by explicit decomposition of the cohomology of Shimura varieties of U(3) using Deligne's (proven) conjecture on the fixed point formula. 606 $aRepresentations of groups 606 $aUnitary groups 606 $aLifting theory 606 $aAutomorphic forms 606 $aTrace formulas 615 0$aRepresentations of groups. 615 0$aUnitary groups. 615 0$aLifting theory. 615 0$aAutomorphic forms. 615 0$aTrace formulas. 676 $a512.22 700 $aFlicker$b Yuval Z$g(Yuval Zvi),$f1955-$01693707 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910953383603321 996 $aAutomorphic representations of low rank groups$94480423 997 $aUNINA