Notes on Jacquet-Langlands' theory = Jacquet-Langlands lǐ lùn 9787040503036, 7040503034

Table of contents :
Commentary on the Jacquet-Langlands Theory -- Robert Langlands
Note on the Genesis of the Book by Jacquet and Langlands -- Herve Jacquet
Preface
Contents
Chapter 1. Representations of the GL_2 Group of a p-adic Field
1. Admissible representations
2. The Kirillov model: preliminary construction
3. The commutativity lemma
4. The finiteness property
5. Whittaker functions
6. A theorem on the contragredient of a representation
7. Supercuspidal representations
8. Introduction to the principal series
9. A lemma on Fourier transforms
10. The principal series and the special representations
11. The equivalence π_{μ_1, μ_2} ~ π_{μ_2, μ_1}
12. The fundamental functional equation
13. Computation of γ_π(χ, s) for the principal series and the special representations
14. The local factors L_π(χ, s)
15. The factors ε_π(χ, s)
16. The case of spherical representations
17. Unitary representations: results
18. Unitary representations: the supercuspidal case
19. Unitaryrepresentations in the principal series
20. Unitary representations: the special case
Chapter 2. The Archimedean Case
1. Admissible representations
2. The representations ρ_{μ_1, μ_2}
3. Irreducible components of ρ_{μ_1, μ_2} (case F = R)
4. Irreducible components of ρ_{μ_1, μ_2} (case F = C)
5. Kirillov model for an irreducible representation
6. The functions L_w(g; χ, s)
7. Factors L_π(χ, s)
8. Factors ε_π(χ, s)
Chapter 3. The Global Theory
1. Parabolic forms
2. Local decomposition of an irreducible representation of G_A
3. The global Hecke algebra
4. Global Whittaker models
5. The multiplicity one theorem
6. Euler product attached to an irreducible representation of G_A
7. The functional equation for L_π(χ, s)
8. The converse of Theorem 4

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