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In mathematics, the Jacquet–Langlands correspondence is a correspondence between automorphic forms on GL2 and its twisted forms, proved by using the Selberg trace formula. It was one of the first examples of the Langlands philosophy that maps between L-groups should induce maps between automorphic representations. There are generalized versions of the Jacquet–Langlands correspondence relating automorphic representations of GL''r''(''D'') and GL''dr''(''F''), where ''D'' is a division algebra of degree ''d''2 over the local or global field ''F''. Suppose that ''G'' is an inner twist of the algebraic group GL2, in other words the multiplicative group of a quaternion algebra. The Jacquet–Langlands correspondence is bijection between *Automorphic representations of ''G'' of dimension greater than 1 *Cuspidal automorphic representations of GL2 that are square integrable (modulo the center) at each ramified place of ''G''. Corresponding representations have the same local components at all unramified places of ''G''. and extended the Jacquet–Langlands correspondence to division algebras of higher dimension. ==References== * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Jacquet–Langlands correspondence」の詳細全文を読む スポンサード リンク
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