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In mathematics, Alvis–Curtis duality is a duality operation on the characters of a reductive group over a finite field, introduced by and studied by his student . introduced a similar duality operation for Lie algebras. Alvis–Curtis duality has order 2 and is an isometry on generalized characters. discusses Alvis–Curtis duality in detail. ==Definition== The dual ζ * of a character ζ of a finite group ''G'' with a split BN-pair is defined to be : Here the sum is over all subsets ''J'' of the set ''R'' of simple roots of the Coxeter system of ''G''. The character ζ is the truncation of ζ to the parabolic subgroup ''P''''J'' of the subset ''J'', given by restricting ζ to ''P''''J'' and then taking the space of invariants of the unipotent radical of ''P''''J'', and ζ is the induced representation of ''G''. (The operation of truncation is the adjoint functor of parabolic induction.) 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「Alvis–Curtis duality」の詳細全文を読む スポンサード リンク
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