 
Summary: Canad. Math. Bull. Vol. 45 (4), 2002 pp. 466482
A Note
on the Automorphic Langlands Group
To Robert Moody on his sixtieth birthday
James Arthur
Abstract. Langlands has conjectured the existence of a universal group, an extension of the absolute
Galois group, which would play a fundamental role in the classification of automorphic representa
tions. We shall describe a possible candidate for this group. We shall also describe a possible candidate
for the complexification of Grothendieck's motivic Galois group.
1
In 1977, Langlands postulated the existence of a universal group in the theory of
automorphic forms [L5]. In Langlands's original formulation, the group would be
an object in the category of complex, reductive, proalgebraic groups. It would be
attached to a given number field F (or more generally, a global field), and would be
an extension of the absolute Galois group
F = Gal( ¯F/F)
( ¯F a fixed algebraic closure of F), by a connected, complex, reductive, proalgebraic
group.
Kottwitz [K2] later pointed out that Langlands's group would be somewhat sim
pler if it were taken in the category of locally compact topological groups. In this for
