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In algebra, an Iwahori subgroup is a subgroup of a reductive algebraic group over a local field that is analogous to a Borel subgroup of an algebraic group. A parahoric subgroup is a subgroup that is a finite union of double cosets of an Iwahori subgroup, so is analogous to a parabolic subgroup of an algebraic group. Iwahori subgroups are named after Nagayoshi Iwahori, and "parahoric" is a portmanteau of "parabolic" and "Iwahori". studied Iwahori subgroups for Chevalley groups over ''p''-adic fields, and extended their work to more general groups. Roughly speaking, an Iwahori subgroup of an algebraic group ''G''(''K''), for a local field ''K'' with integers ''O'' and residue field ''k'', is the inverse image in ''G''(''O'') of a Borel subgroup of ''G''(''k''). A reductive group over a local field has a Tits system (''B'',''N''), where ''B'' is a parahoric group, and the Weyl group of the Tits system is an affine Coxeter group. ==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「Iwahori subgroup」の詳細全文を読む スポンサード リンク
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