Kirillov model
In mathematics, the Kirillov model, studied by , is a realization of a representation of "GL" over a local field on a space of functions on the local field. If "G" is the algebraic group "GL" 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 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" of a vector ξ of the Kirillov model by where π("g") is the image of "g" in the Kirillov model.