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The descent map from automorphic representations of GL(n) to classical groups [[electronic resource] /] / David Ginzburg, Stephen Rallis, David Soudry
| The descent map from automorphic representations of GL(n) to classical groups [[electronic resource] /] / David Ginzburg, Stephen Rallis, David Soudry |
| Autore | Ginzburg D (David) |
| Pubbl/distr/stampa | Singapore, : World Scientific Pub., c2011 |
| Descrizione fisica | 1 online resource (350 p.) |
| Disciplina |
512.73
515.9 |
| Altri autori (Persone) |
RallisStephen
SoudryDavid |
| Soggetto topico |
L-functions
Automorphic forms Representations of groups |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-43339-7
9786613433398 981-4304-99-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910457559303321 |
Ginzburg D (David)
|
||
| Singapore, : World Scientific Pub., c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The descent map from automorphic representations of GL(n) to classical groups [[electronic resource] /] / David Ginzburg, Stephen Rallis, David Soudry
| The descent map from automorphic representations of GL(n) to classical groups [[electronic resource] /] / David Ginzburg, Stephen Rallis, David Soudry |
| Autore | Ginzburg D (David) |
| Pubbl/distr/stampa | Singapore, : World Scientific Pub., c2011 |
| Descrizione fisica | 1 online resource (350 p.) |
| Disciplina |
512.73
515.9 |
| Altri autori (Persone) |
RallisStephen
SoudryDavid |
| Soggetto topico |
L-functions
Automorphic forms Representations of groups |
| ISBN |
1-283-43339-7
9786613433398 981-4304-99-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910778817603321 |
|
Ginzburg D (David)
|
||
| Singapore, : World Scientific Pub., c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The descent map from automorphic representations of GL(n) to classical groups / / David Ginzburg, Stephen Rallis, David Soudry
| The descent map from automorphic representations of GL(n) to classical groups / / David Ginzburg, Stephen Rallis, David Soudry |
| Autore | Ginzburg D (David) |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore, : World Scientific Pub., c2011 |
| Descrizione fisica | 1 online resource (350 p.) |
| Disciplina |
512.73
515.9 |
| Altri autori (Persone) |
RallisStephen
SoudryDavid |
| Soggetto topico |
L-functions
Automorphic forms Representations of groups |
| ISBN |
1-283-43339-7
9786613433398 981-4304-99-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910820948003321 |
|
Ginzburg D (David)
|
||
| Singapore, : World Scientific Pub., c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
L functions for the orthogonal group / / D. Ginzburg, I. Piatetski-Shapiro, S. Rallis
| L functions for the orthogonal group / / D. Ginzburg, I. Piatetski-Shapiro, S. Rallis |
| Autore | Ginzburg D (David) |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1997 |
| Descrizione fisica | 1 online resource (233 p.) |
| Disciplina |
510 s
512/.74 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
L-functions
Automorphic functions Linear algebraic groups |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0196-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table of Contents""; ""Â0. Introduction""; ""Â1. Basic Data""; ""Â2. Support Ideals""; ""Â3. Certain Jacquet Functors""; ""Â4. Global Theory""; ""Â4.1 Global Theory""; ""Â4.2 Spherical-Whittaker Case (I)""; ""Â4.3 Spherical-Whittaker Models (II)""; ""Â5. Support Ideals (II)""; ""Â6. Calculation of local factors""; ""Â7. Determination of γ-factors (Spherical Case)""; ""Â8. Determination of γ-factors (Spherical-Whittaker Case)""; ""Â9 Bibliography"" |
| Record Nr. | UNINA-9910480988003321 |
|
Ginzburg D (David)
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
L functions for the orthogonal group / / D. Ginzburg, I. Piatetski-Shapiro, S. Rallis
| L functions for the orthogonal group / / D. Ginzburg, I. Piatetski-Shapiro, S. Rallis |
| Autore | Ginzburg D (David) |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1997 |
| Descrizione fisica | 1 online resource (233 p.) |
| Disciplina |
510 s
512/.74 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
L-functions
Automorphic functions Linear algebraic groups |
| ISBN | 1-4704-0196-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table of Contents""; ""Â0. Introduction""; ""Â1. Basic Data""; ""Â2. Support Ideals""; ""Â3. Certain Jacquet Functors""; ""Â4. Global Theory""; ""Â4.1 Global Theory""; ""Â4.2 Spherical-Whittaker Case (I)""; ""Â4.3 Spherical-Whittaker Models (II)""; ""Â5. Support Ideals (II)""; ""Â6. Calculation of local factors""; ""Â7. Determination of γ-factors (Spherical Case)""; ""Â8. Determination of γ-factors (Spherical-Whittaker Case)""; ""Â9 Bibliography"" |
| Record Nr. | UNINA-9910788732403321 |
|
Ginzburg D (David)
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
L functions for the orthogonal group / / D. Ginzburg, I. Piatetski-Shapiro, S. Rallis
| L functions for the orthogonal group / / D. Ginzburg, I. Piatetski-Shapiro, S. Rallis |
| Autore | Ginzburg D (David) |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1997 |
| Descrizione fisica | 1 online resource (233 p.) |
| Disciplina |
510 s
512/.74 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
L-functions
Automorphic functions Linear algebraic groups |
| ISBN | 1-4704-0196-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table of Contents""; ""Â0. Introduction""; ""Â1. Basic Data""; ""Â2. Support Ideals""; ""Â3. Certain Jacquet Functors""; ""Â4. Global Theory""; ""Â4.1 Global Theory""; ""Â4.2 Spherical-Whittaker Case (I)""; ""Â4.3 Spherical-Whittaker Models (II)""; ""Â5. Support Ideals (II)""; ""Â6. Calculation of local factors""; ""Â7. Determination of γ-factors (Spherical Case)""; ""Â8. Determination of γ-factors (Spherical-Whittaker Case)""; ""Â9 Bibliography"" |
| Record Nr. | UNINA-9910829045703321 |
|
Ginzburg D (David)
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||