LEADER 05640nam 2200757 a 450 001 9910969574603321 005 20250303232724.0 010 $a9786613433398 010 $a9781283433396 010 $a1283433397 010 $a9789814304993 010 $a9814304999 035 $a(CKB)2550000000079811 035 $a(EBL)840649 035 $a(OCoLC)858228212 035 $a(SSID)ssj0000645456 035 $a(PQKBManifestationID)12260388 035 $a(PQKBTitleCode)TC0000645456 035 $a(PQKBWorkID)10682670 035 $a(PQKB)11119063 035 $a(MiAaPQ)EBC840649 035 $a(WSP)00001428 035 $a(Au-PeEL)EBL840649 035 $a(CaPaEBR)ebr10524632 035 $a(CaONFJC)MIL343339 035 $a(Perlego)849219 035 $a(EXLCZ)992550000000079811 100 $a20110929d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe descent map from automorphic representations of GL(n) to classical groups /$fDavid Ginzburg, Stephen Rallis, David Soudry 205 $a1st ed. 210 $aSingapore $cWorld Scientific Pub.$dc2011 215 $a1 online resource (350 p.) 300 $aDescription based upon print version of record. 311 08$a9789814304986 311 08$a9814304980 320 $aIncludes bibliographical references (p. 335-338) and index. 327 $aPreface; Contents; 1. Introduction; 1.1 Overview; 1.2 Formulas for the Weil representation; 1.3 The case, where H is unitary and the place v splits in E; 2. On Certain Residual Representations; 2.1 The groups; 2.2 The Eisenstein series to be considered; 2.3 L-groups and representations related to P; 2.4 The residue representation; 2.5 The case of a maximal parabolic subgroup (r = 1); 2.6 A preliminary lemma on Eisenstein series on GLn; 2.7 Constant terms of E(h, f , ); 2.8 Description of W(M ,D ); 2.9 Continuation of the proof of Theorem 2.1 327 $a3. Coefficients of Gelfand-Graev Type, of Fourier-Jacobi Type, and Descent3.1 Gelfand-Graev coefficients; 3.2 Fourier-Jacobi coefficients; 3.3 Nilpotent orbits; 3.4 Global integrals representing L-functions I; 3.5 Global integrals representing L-functions II; 3.6 Definition of the descent; 3.7 Definition of Jacquet modules corresponding to Gelfand-Graev characters; 3.8 Definition of Jacquet modules corresponding to Fourier-Jacobi characters; 4. Some double coset decompositions; 4.1 The space Q \h (V ) /Q; 1. The case where K is a field; 2. The case where K = k k 327 $a4.2 A set of representatives for Q \h(V ) /Q1. The case where K is a field and h(Vk) is not even orthogonal and split; 2. The case where h(Vk) is even orthogonal and split; 3. The case K = k k; 4.3 Stabilizers; 1. The case where K is a field and h(V ) is not even orthogonal and split; 2. The case where h(V ) is even orthogonal and split; 3. The case K = k k; 4.4 The set Q\h(W , ) /L ,; 1. The case where K is a field and w is anisotropic; 2. The case where K = k k (and w - anisotropic); 5. Jacquet modules of parabolic inductions: Gelfand-Graev characters 327 $a5.1 The case where K is a field5.2 The case K = k k; 6. Jacquet modules of parabolic inductions: Fourier-Jacobi characters; 6.1 The case where K is a field; 6.2 The case K = k k; 7. The tower property; 7.1 A general lemma on "exchanging roots"; 7.2 A formula for constant terms of Gelfand-Graev coefficients; 7.3 Global Gelfand-Graev models for cuspidal representations; 7.4 The general case: H is neither split nor quasi-split; 7.5 Global Gelfand-Graev models for the residual representations E; 7.6 A formula for constant terms of Fourier-Jacobi coefficients 327 $a7.7 Global Fourier-Jacobi models for cuspidal representations7.8 Global Fourier-Jacobi models for the residual representations E; 8. Non-vanishing of the descent I; 8.1 The Fourier coefficient corresponding to the partition (m,m,m' - 2m); 8.2 Conjugation of Sm by the element ?; 8.3 Exchanging the roots y , and x , (dim V = 2m , m > 2); 8.4 First induction step: exchanging the roots y and x , , for 1 i j [m+1 ]; dim V = 2m; 8.5 First induction step: odd orthogonal groups; 8.6 Second induction step: exchanging the roots y and x , , for i + j m+ 1, j > [m+1 ] (dim V = 2m) 327 $a8.7 Completion of the proof of Theorems 8.1, 8.2 330 $aThis book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of Gelfand-Graev type, or of Fourier-Jacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in 606 $aL-functions 606 $aAutomorphic forms 606 $aRepresentations of groups 615 0$aL-functions. 615 0$aAutomorphic forms. 615 0$aRepresentations of groups. 676 $a512.73 676 $a515.9 700 $aGinzburg$b D$g(David)$0725891 701 $aRallis$b Stephen$f1942-$056906 701 $aSoudry$b David$f1956-$0319153 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910969574603321 996 $aThe descent map from automorphic representations of GL(n) to classical groups$94329629 997 $aUNINA