Published online by Cambridge University Press: 20 December 2011
For V a two-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 paper, 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 semisimple with distinct Hodge–Tate weights; this proves a conjecture of Breuil. Using this result, we verify Emerton’s conjecture that dim Ref η⊗ψ (V )=dim Exp η∣⋅∣⊗xψ (B (V )an ⊗(x∣⋅∣∘det )) for those V which are irreducible, crystabelian and Frobenius semisimple.