# memo_has_moved_text();Descent Construction for GSpin groups

Joseph Hundley and Eitan Sayag

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 243, Number 1148
ISBNs: 978-1-4704-1667-6 (print); 978-1-4704-3444-1 (online)
DOI: http://dx.doi.org/10.1090/memo/1148
Published electronically: June 20, 2016
Keywords:Langlands functoriality, descent, unipotent integration

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Chapters

• Chapter 1. Introduction

Part 1. General matters

• Chapter 2. Some notions related to Langlands functoriality
• Chapter 3. Notation
• Chapter 4. The Spin groups $GSpin_m$ and their quasisplit forms
• Chapter 5. “Unipotent periods”

Part 2. Odd case

• Chapter 6. Notation and statement
• Chapter 7. Unramified correspondence
• Chapter 8. Eisenstein series I: Construction and main statements
• Chapter 9. Descent construction
• Chapter 10. Appendix I: Local results on Jacquet functors
• Chapter 11. Appendix II: Identities of unipotent periods

Part 3. Even case

• Chapter 12. Formulation of the main result in the even case
• Chapter 13. Notation
• Chapter 14. Unramified correspondence
• Chapter 15. Eisenstein series
• Chapter 16. Descent construction
• Chapter 17. Appendix III: Preparations for the proof of Theorem 15.0.12
• Chapter 18. Appendix IV: Proof of Theorem 15.0.12
• Chapter 19. Appendix V: Auxilliary results used to prove Theorem 15.0.12
• Chapter 20. Appendix VI: Local results on Jacquet functors
• Chapter 21. Appendix VII: Identities of unipotent periods

### Abstract

In this paper we provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of essentially self-dual representations, that is representations which are isomorphic to the twist of their own contragredient by some Hecke character. Our theory supplements the recent work of Asgari-Shahidi on the functorial lift from (split and quasisplit forms of) $GSpin_{2}n$ to $GL_{2}n.$