An irreducible smooth non-admissible representation

G.F. Helminck

doi:10.1016/0019-3577(90)90011-B

An irreducible smooth non-admissible representation

G.F. Helminck

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Abstract

It is shown for the group of k-rational points of an affine algebraic group G with k a finite extension of Qp that the topological irreducibility of unitary representations of G does not have to be equivalent to the algebraic irreducibility of the representation on the smooth vectors. We give for a specific G an example of an irreducible smooth representation, which is not admissible.

Original language	English
Pages (from-to)	435-438
Number of pages	4
Journal	Indagationes mathematicae
Volume	1
Issue number	4
DOIs	https://doi.org/10.1016/0019-3577(90)90011-B
Publication status	Published - 1990

Keywords

IR-97361

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10.1016/0019-3577(90)90011-B

Helminck90irreducibleFinal published version, 158 KB

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abstract = "It is shown for the group of k-rational points of an affine algebraic group G with k a finite extension of Qp that the topological irreducibility of unitary representations of G does not have to be equivalent to the algebraic irreducibility of the representation on the smooth vectors. We give for a specific G an example of an irreducible smooth representation, which is not admissible.",

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T1 - An irreducible smooth non-admissible representation

AU - Helminck, G.F.

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AB - It is shown for the group of k-rational points of an affine algebraic group G with k a finite extension of Qp that the topological irreducibility of unitary representations of G does not have to be equivalent to the algebraic irreducibility of the representation on the smooth vectors. We give for a specific G an example of an irreducible smooth representation, which is not admissible.

KW - IR-97361

U2 - 10.1016/0019-3577(90)90011-B

DO - 10.1016/0019-3577(90)90011-B

M3 - Article

SN - 0019-3577

VL - 1

SP - 435

EP - 438

JO - Indagationes mathematicae

JF - Indagationes mathematicae

IS - 4

ER -

An irreducible smooth non-admissible representation

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