Locally analytic vectors of unitary principal series of GL2(Qp) I
نویسنده
چکیده
For V a 2-dimensional p-adic representation of GQp , we denote by B(V ) the admissible unitary representation of GL2(Qp) attached to V under the p-adic local Langlands correspondence of GL2(Qp) initiated by Breuil. In this article, building on the works of Berger-Breuil and Colmez, we determine the locally analytic vectors B(V )an of B(V ) when V is irreducible, crystabelian and Frobenius semi-simple with Hodge-Tate weights (0, k − 1) for some integer k ≥ 2; this proves a conjecture of Breuil. Using this result, we verify Emerton’s conjecture that dimRef(V ) = dimExp = (B(V )an ⊗ (x| · | ◦ det)) for those V ∈ S cris ∗ which are not exceptional.
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