THE JACQUET-LANGLANDS CORRESPONDENCE FOR GL2 Contents
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چکیده
1.1. Matching regular semisimple conjugacy classes. Let X(F ) = F × F×, viewed as the space of semisimple conjugacy classes in GL2(F ) via GL2(F ) → X(F ) sending γ 7→ (Tr(γ),det(γ)). Similarly we have D× → X(F ) sending γ′ 7→ (TrD/F (γ),NmD/F (γ′)), where TrD/F and NmD/F mean reduced trace and norm. For regular semisimple γ ∈ GL2(F ) and γ′ ∈ D×, we write γ ∼ γ′ if they have the same image in X(F ). This gives a bijection beween elliptic regular semisimple classes in GL2(F ) and regular semisimple classes in D×. Let ω : F× → C× be a smooth character.
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