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 representations. 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.

MSC Classifications:

11R39, 22E55 show english descriptions Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
Representations of Lie and linear algebraic groups over global fields and adele rings [See also 20G05] 11R39 - Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
22E55 - Representations of Lie and linear algebraic groups over global fields and adele rings [See also 20G05]

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