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- Kirillov_model abstract "In mathematics, the Kirillov model, studied by Kirillov (1963), is a realization of a representation of GL2 over a local field on a space of functions on the local field.If G is the algebraic group GL2 and F is a non-Archimedean local field,and τ is a fixed nontrivial character of the additive group of Fand 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 Jacquet & Langlands (1970) 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 Wξ of a vector ξ of the Kirillov model byWξ(g) = π(g)ξ(1)where π(g) is the image of g in the Kirillov model.Bernstein (1984) defined the Kirillov model for the general linear group GLn using the mirabolic subgroup. More precisely, a Kirillov model for a representation of the mirabolic 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.".
- Kirillov_model wikiPageExternalLink book.
- Kirillov_model wikiPageID "20671987".
- Kirillov_model wikiPageRevisionID "447613835".
- Kirillov_model hasPhotoCollection Kirillov_model.
- Kirillov_model subject Category:Automorphic_forms.
- Kirillov_model subject Category:Langlands_program.
- Kirillov_model subject Category:Representation_theory.
- Kirillov_model type Abstraction100002137.
- Kirillov_model type AutomorphicForms.
- Kirillov_model type Form106290637.
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- Kirillov_model comment "In mathematics, the Kirillov model, studied by Kirillov (1963), is a realization of a representation of GL2 over a local field on a space of functions on the local field.If G is the algebraic group GL2 and F is a non-Archimedean local field,and τ is a fixed nontrivial character of the additive group of Fand 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 Jacquet & Langlands (1970) showed that an irreducible representation of dimension greater than 1 has an essentially unique Kirillov model. ".
- Kirillov_model label "Kirillov model".
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- Kirillov_model isPrimaryTopicOf Kirillov_model.