104
reads

Ruochuan Liu

2010-07-14
15:40:00 - 17:00:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

The p-adic local Langlands correspondence for GL₂(Q_p), which is initiated by Breuil and established by Colmez, attaches an admissible unitary representation Π(V) of GL₂(Q_p) to any 2-dimensional irreducible representation V of G_Qp. The unitary principal series of GL₂(Q_p) are those admissible unitary representations corresponding to trianguline representations. Although the present version of the p-adic local Langlands correspondence for GL₂(Q_p) is formulated at the level of admissible unitary representations, it is very useful, as in Breuil's original works (and many other examples), to have the information of the space of locally analytic vectors Π(V)_an of Π(V). The main result of this talk is a determination of the space of locally analytic vectors for all (non-exceptional) unitary principle series of GL₂(Q_p); this proves a conjecture of Emerton. This is a joint work with Bingyong Xie and Yuancao Zhang.