Chapter
1.2. Self dual representations of 𝐺𝐿_{𝑛}(\A) and the descent method
1.4. Descent construction for essentially self dual representations
1.6. The descent construction and the structure of the argument
1.7. Structure of the paper
Chapter 2. Some notions related to Langlands functoriality
2.2. Essentially self-dual: 𝜂-orthogonal and 𝜂-symplectic
3.2. Notions of “genericity”
Chapter 4. The Spin groups 𝐺𝑆𝑝𝑖𝑛_{𝑚} and their quasisplit forms
4.1. Similitude groups 𝐺𝑆𝑝_{2𝑛},𝐺𝑆𝑂_{2𝑛}
4.2. Definition of split 𝐺𝑆𝑝𝑖𝑛
4.3. Definition of quasi-split 𝐺𝑆𝑝𝑖𝑛
4.4. Unipotent subgroups of 𝐺𝑆𝑝𝑖𝑛_{𝑚} and their characters
Chapter 5. “Unipotent periods”
5.1. A lemma regarding unipotent periods
5.2. Relation of unipotent periods via theta functions
Chapter 6. Notation and statement
6.2. Weyl group of 𝐺𝑆𝑝𝑖𝑛_{2𝑚}; its action on standard Levis and their representations
Chapter 7. Unramified correspondence
Chapter 8. Eisenstein series I: Construction and main statements
Chapter 9. Descent construction
9.1. Vanishing of deeper descents and the descent representation
9.3. Proof of main theorem
Chapter 10. Appendix I: Local results on Jacquet functors
Chapter 11. Appendix II: Identities of unipotent periods
11.1. A lemma regarding the projection, and a remark
11.2. Relations among unipotent periods used in Theorem 9.2.1
Chapter 12. Formulation of the main result in the even case
13.2. Weyl group of 𝐺𝑆𝑝𝑖𝑛_{2𝑚+1}; its action on standard Levis and their representations
Chapter 14. Unramified correspondence
Chapter 15. Eisenstein series
Chapter 16. Descent construction
16.1. Vanishing of deeper descents and the descent representation
16.2. Vanishing of incompatible descents
16.4. Proof of the main theorem (Even case)
Chapter 17. Appendix III: Preparations for the proof of Theorem 15.0.12
17.1. Poles on Hyperplanes
17.2. Intertwining operators
17.3. Reduction to relative rank one situation
Chapter 18. Appendix IV: Proof of Theorem 15.0.12
Chapter 19. Appendix V: Auxilliary results used to prove Theorem 15.0.12
19.1. Proof of Lemma 17.3.3
19.2. Proof of Proposition 17.2.1
19.3. Proof of Proposition 18.0.4
19.4. Proof of Proposition 18.0.6
Chapter 20. Appendix VI: Local results on Jacquet functors
Chapter 21. Appendix VII: Identities of unipotent periods
Descent Construction for GSpin Groups
( Memoirs of the American Mathematical Society )
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