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Let F be a local field of residual characteristic p, and ρ a smooth irreducible representation of GL2(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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