Locally analytic vectors of unitary principal series of GL₂(Qp)

2011/03/13 by Liu, Ruochuan, Xie, Bingyong, Zhang, Yuancao
#11F70 #11F80 #11F85 #22E35 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1103.2543

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.

Related

• The p-adic local Langlands correspondence for GL₂(Q_p)
• Equations differentielles p-adiques et modules de Jacquet analytiques
• Ordinary local representations and \Ext groups
• Strong local-global compatibility in the p-adic Langlands program for U(2)
• Fonctions d'une variable p-adique et représentations de \rm GL₂(Q_p)