Locally analytic vectors of unitary principal series of GL_2(Qp)

Abstract

The p-adic local Langlands correspondence for GL2(Qp) attaches to any 2-dimensional irreducible p-adic representation V of the absolute Galois groups of Qp an admissible unitary representation Pi(V) of GL2(Qp). The unitary principal series of GL2(Qp) are those Pi(V) corresponding to trianguline representations. In this article, for p>2, using the machinery of Colmez, we determine the space of locally analytic vectors for all non-exceptional unitary principal series of GL2(Qp) by proving a conjecture of Emerton.

Final version

References in corpus (1)

• Slope filtrations for relative Frobenius

Cited by in corpus (6)

• The p-adic local Langlands correspondence for GL_2(Q_p)
• Extensions de représentations de de Rham et vecteurs localement algébriques
• Endomorphism algebras of admissible p-adic representations of p-adic Lie groups
• Higher $\mathcal{L}$-invariants for ${\mathrm{GL}}_3({\mathbb{Q}}_p)$ and local-global compatibility
• Sur un problème de compatibilité local-global localement analytique
• Derivatives of Frobenius and Derivatives of Hodge weights