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GENERIC TRANSFER FOR GENERAL SPIN GROUPS MAHDI ASGARI and FREYDOON SHAHIDI
 

Summary: GENERIC TRANSFER FOR GENERAL SPIN GROUPS
MAHDI ASGARI and FREYDOON SHAHIDI
Abstract
We prove Langlands functoriality for the generic spectrum of general spin groups
(both odd and even). Contrary to other recent instances of functoriality, our resulting
automorphic representations on the general linear group are not self-dual. Together
with cases of classical groups, this completes the list of cases of split reductive groups
whose L-groups have classical derived groups. The important transfer from GSp4 to
GL4 follows from our result as a special case.
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
2. Structure theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3. Analytic properties of local L-functions . . . . . . . . . . . . . . . . . . 150
4. Stability of -factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5. Analytic properties of global L-functions . . . . . . . . . . . . . . . . . 175
6. Proof of the main theorem . . . . . . . . . . . . . . . . . . . . . . . . . 176
7. Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
1. Introduction
Let G be a connected reductive group over a number field k. Let G = G(A), where A

  

Source: Asgari, Mahdi - Department of Mathematics, Oklahoma State University

 

Collections: Mathematics