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In representation theory, a branch of mathematics, the Whittaker model is a realization of a representation of a reductive algebraic group such as ''GL''2 over a finite or local or global field on a space of functions on the group. It is named after E. T. Whittaker even though he never worked in this area, because pointed out that for the group SL2(R) some of the functions involved in the representation are Whittaker functions. Irreducible representations without a Whittaker model are sometimes called "degenerate", and those with a Whittaker model are sometimes called "generic". The representation θ10 of the symplectic group Sp4 is the simplest example of a degenerate representation. ==Whittaker models for GL2== If ''G'' is the algebraic group ''GL''2 and F is a local field, and τ is a fixed non-trivial character of the additive group of F and π is an irreducible representation of a general linear group ''G''(F), then the Whittaker model for π is a representation π on a space of functions ''f'' on ''G''(F) satisfying : used Whittaker models to assign L-functions to admissible representations of ''GL''2. 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「Whittaker model」の詳細全文を読む スポンサード リンク
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