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In mathematics, the Kirillov model, studied by , is a realization of a representation of ''GL''2 over a local field on a space of functions on the local field. If ''G'' is the algebraic group ''GL''2 and F is a non-Archimedean local field, and τ is a fixed nontrivial character of the additive group of F and π is an irreducible representation of ''G''(F), then the Kirillov model for π is a representation π on a space of locally constant functions ''f'' on F * with compact support in F such that : showed that an irreducible representation of dimension greater than 1 has an essentially unique Kirillov model. Over a local field, the space of functions with compact support in ''F * has codimension 0, 1, or 2 in the Kirillov model, depending on whether the irreducible representation is cuspidal, special, or principal. The Whittaker model can be constructed from the Kirillov model, by defining the image ''W''ξ of a vector ξ of the Kirillov model by :''W''ξ(''g'') = π(g)ξ(1) where π(''g'') is the image of ''g'' in the Kirillov model. defined the Kirillov model for the general linear group GL''n'' using the mirabolic subgroup. More precisely, a Kirillov model for a representation of the general linear group is an embedding of it in the representation of the mirabolic group induced from a non-degenerate character of the group of upper triangular matrices. ==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「Kirillov model」の詳細全文を読む スポンサード リンク
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