In mathematics, the Kirillov model, studied by Kirillov (1963), 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 
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 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.