Kirillov models and integral structures in p-adic smooth representations of GL 2(F)

David Kazhdan; Ehud de Shalit

doi:10.1016/j.jalgebra.2011.12.017

Kirillov models and integral structures in p-adic smooth representations of GL ₂(F)

David Kazhdan
, Ehud de Shalit^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let F be a local field of residual characteristic p, and ρ a smooth irreducible representation of GL ₂(F), realized over the algebraic closure of Qp. Studying its Kirillov model, we exhibit a necessary and sufficient criterion for the existence of an integral structure in ρ. We apply our criterion to tamely ramified principal series, and get a new proof of a theorem of M.-F. Vigneras.

Original language	English
Pages (from-to)	212-223
Number of pages	12
Journal	Journal of Algebra
Volume	353
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.12.017
State	Published - 1 Mar 2012

Keywords

Integral structures
Smooth representations

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10.1016/j.jalgebra.2011.12.017

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abstract = "Let F be a local field of residual characteristic p, and ρ a smooth irreducible representation of GL 2(F), realized over the algebraic closure of Qp. Studying its Kirillov model, we exhibit a necessary and sufficient criterion for the existence of an integral structure in ρ. We apply our criterion to tamely ramified principal series, and get a new proof of a theorem of M.-F. Vigneras.",

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N2 - Let F be a local field of residual characteristic p, and ρ a smooth irreducible representation of GL 2(F), realized over the algebraic closure of Qp. Studying its Kirillov model, we exhibit a necessary and sufficient criterion for the existence of an integral structure in ρ. We apply our criterion to tamely ramified principal series, and get a new proof of a theorem of M.-F. Vigneras.

AB - Let F be a local field of residual characteristic p, and ρ a smooth irreducible representation of GL 2(F), realized over the algebraic closure of Qp. Studying its Kirillov model, we exhibit a necessary and sufficient criterion for the existence of an integral structure in ρ. We apply our criterion to tamely ramified principal series, and get a new proof of a theorem of M.-F. Vigneras.

KW - Integral structures

KW - Smooth representations

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Kirillov models and integral structures in p-adic smooth representations of GL ₂(F)

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Keywords

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