ON A GROUP CLOSELY RELATED WITH THE AUTOMORPHIC LANGLANDS GROUP

Abstract

. Let L K denote the hypothetical automorphic Langlands gr- oup of a number field K . In our recent study, we briefly introduced a certain unconditional non-commutative topological group W A ϕ K , called the Weil-Arthur id`ele group of K , which, assuming the existence of L K , comes equipped with a natural topological group homomorphism NR ϕ Langlands K : W A ϕ K → L K that we called the “Langlands form” of the global nonabelian norm-residue symbol of K . In this work, we present a detailed construction of W A ϕ K and NR ϕ Langlands K : W A ϕ K → L K , and discuss their basic properties.