Descent Construction for GSpin Groups

ISBN-13: 9781470416676 / Angielski

Joseph Hundley;Eitan Sayag

Opis

In this paper the authors 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. The authors' theory supplements the recent work of Asgari-Shahidi on the functorial lift from (split and quasisplit forms of) $GSpin_$ to $GL_$.

Spis treści

• Introduction
• Part 1. General matters: Some notions related to Langlands functoriality
• Notation
• The Spin groups $GSpin_$ and their quasisplit forms
• ``Unipotent periods''
• Part 2. Odd case: Notation and statement
• Unramified correspondence
• Eisenstein series I: Construction and main statements
• Descent construction
• Appendix I: Local results on Jacquet functors
• Appendix II: Identities of unipotent periods
• Part 3. Even case: Formulation of the main result in the even case
• Notation
• Unramified correspondence
• Eisenstein series
• Descent construction
• Appendix III: Preparations for the proof of Theorem 15.0.12
• Appendix IV: Proof of Theorem 15.0.12
• Appendix V: Auxiliary results used to prove Theorem 15.0.12
• Appendix VI: Local results on Jacquet functors
• Appendix VII: Identities of unipotent periods
• Bibliography.