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FUNCTORIALITY FOR GENERAL SPIN GROUPS MAHDI ASGARI AND FREYDOON SHAHIDI
 

Summary: FUNCTORIALITY FOR GENERAL SPIN GROUPS
MAHDI ASGARI AND FREYDOON SHAHIDI
Abstract. We establish the functorial transfer of generic, automorphic representations
from the quasi-split general spin groups to general linear groups over arbitrary number
fields, completing an earlier project. Our results are definitive and, in particular, we
determine the image of this transfer completely and give a number of applications.
1. Introduction
In this article we complete a project we started in [AS1] by establishing the full transfer of
generic, automorphic representations from the quasi-split general spin groups to the general
linear group. In particular, we completely determine the image of this transfer.
Our first main result is to establish the transfer of globally generic, automorphic represen-
tations from the quasi-split non-split even general spin group, GSpin
(2n, Ak), to GL(2n, Ak)
(cf. Theorem 3.3). Here, k denotes an arbitrary number field. We proved the analogous
result for the split groups GSpin(2n) and GSpin(2n + 1) in [AS1], but were not able to
prove the quasi-split case then since the "stability of root numbers" was not yet available
for non-split groups.
Our next main result is to prove that the transferred representation to GL(2n), from either
an even or an odd general spin group, is actually an isobaric, automorphic representation
(cf. Theorem 5.11).

  

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

 

Collections: Mathematics