The descent map from automorphic representations of GL(n) to classical groups /

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Bibliographic Details
Author / Creator:	Ginzburg, D. (David)
Imprint:	Singapore ; Hackensack, NJ : World Scientific Pub., c2011.
Description:	ix, 339 p. : ill. ; 26 cm.
Language:	English
Subject:	L-functions. Automorphic forms. Representations of groups. Automorphic forms. L-functions. Representations of groups.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/8513946

Hidden Bibliographic Details
Other authors / contributors:	Rallis, Stephen, 1942- Soudry, David, 1956-
ISBN:	9789814304986 9814304980
Notes:	Includes bibliographical references (p. 335-338) and index.

Table of Contents:

Preface
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 GL n
2.7. Constant terms of E (h, f ¿,s )
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 Descent
3.1. 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 Qj\h(V)k/Qz
4.2. A set of representatives for Qj\h(V)k/Qe
4.3. Stabilizers
4.4. The set Q\h(Wm, l)k/Ll, wo
5. Jacquet modules of parabolic inductions: Gelfand-Graev characters
5.1. The case where K is a field
5.2. 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 r
7.6. A formula for constant terms of Fourier-Jacobi coefficients
7.7. Global Fourier-Jacobi models for cuspidal representations
7.8. Global Fourier-Jacobi models for the residual representations E r
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 ±_m
8.3. Exchanging the roots y1,2 and x1,1 (dimEV = 2m , m > 2)
8.4. First induction step: exchanging the roots yi, j and Xj-iti, for 1
8.5. First induction step: odd orthogonal groups
8.6. Second induction step: exchanging the roots yi, j and xj-i, i, for i + j [3*P\ (dmiEV = 2m)
8.7. Completion of the proof of Theorems 8.1, 8.2; dimEV = 2m
8.8. Completion of the proof of Theorem 8.3
8.9. Second induction step: odd orthogonal groups
8.10. Completion of the proof of Theorems 8.1, 8.2; h(V) odd orthogonal
9. Non-vanishing of the descent II
9.1. The case HA = Sp4n+2(A)
9.2. The case H = SO4n+1
9.3. Whittaker coefficients of the descent corresponding to Gelfand Graev coefficients: the unipotent group and its character; h{{V) $$$ S04n+1
9.4. Conjugation by the element fjm
9.5. Exchanging roots: h(V) = S04N, U4n
9.6. Nonvanishing of the Whittaker coefficient of the descent corresponding to Gelfand-Graev coefficients: h(V) = S04n, U4n
9.7. Nonvanishing of the Whittaker coefficient of the descent corresponding to Gelfand-Graev coefficients: h(V) = U4n+2, So4n+3
9.8. The Whittaker coefficient of the descent corresponding to Fourier-Jacobi coefficients: Ha ^ Sp4n+2(A)
9.9. The nonvanishing of the Whittaker coefficient of the descent corresponding to Fourier-Jacobi coefficients: HA=Sp4n(A)Sp4n(A), U4n(A)
9.10. Nonvanishing of the Whittaker coefficient of the descent corresponding to Fourier-Jacobi coefficients: h(V) = U4n+2
10. Global genericity of the descent and global integrals
10.1. Statement of the theorems
10.2. Proof of Theorem 10.3
10.3. Proof of Theorem 10.4
10.4. A family of dual global integrals I
10.5. A family of dual global integrals II
10.6. L-functions
11. Langlands (weak) functorial lift and descent
11.1. The cuspidal part of the weak lift
11.2. The image of the weak lift
11.3. On generalized endoscopy
11.4. Base change
11.5. Automorphic induction
Bibliography
Index

The descent map from automorphic representations of GL(n) to classical groups /

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