| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910969574603321 |
|
|
Autore |
Ginzburg D (David) |
|
|
Titolo |
The descent map from automorphic representations of GL(n) to classical groups / / David Ginzburg, Stephen Rallis, David Soudry |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Singapore, : World Scientific Pub., c2011 |
|
|
|
|
|
|
|
ISBN |
|
9786613433398 |
9781283433396 |
1283433397 |
9789814304993 |
9814304999 |
|
|
|
|
|
|
|
|
Edizione |
[1st ed.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (350 p.) |
|
|
|
|
|
|
Altri autori (Persone) |
|
RallisStephen <1942-> |
SoudryDavid <1956-> |
|
|
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
|
|
Soggetti |
|
L-functions |
Automorphic forms |
Representations of groups |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Description based upon print version of record. |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references (p. 335-338) and index. |
|
|
|
|
|
|
Nota di contenuto |
|
Preface; 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 |
3. 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 |
4.2 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 |
5.1 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 |
7.7 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 α; 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) |
8.7 Completion of the proof of Theorems 8.1, 8.2 |
|
|
|
|
|
|
Sommario/riassunto |
|
This 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 |
|
|
|
|
|
|
|
| |