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Descent Construction for GSpin groups

About this Title

Joseph Hundley, Department of Mathematics, 244 Mathematics Building, University at Buffalo, Buffalo, NY 14260-2900 and Eitan Sayag, Department of Mathematics , Ben Gurion University of the Negev , P.O.B. 653 , Be’er Sheva 8410501, ISRAEL

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)
Published electronically: April 12, 2016
Keywords: Langlands functoriality, descent, unipotent integration
MSC: Primary 11F70, 11F55

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Table of Contents


  • 1. Introduction

1. General matters

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

2. Odd case

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

3. Even case

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


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) $GSpin_{2n}$ to $GL_{2n}.$

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