Rigid analytic vectors of crystalline representations arising in p-adic Langlands

Let B ( V ) be the admissible unitary G L 2 Q p -representation associated to two dimensional crystalline Galois representation by -adic Langlands constructed Breuil. Berger and Breuil conjectured an explicit description of locally analytic vectors la which is now proved Liu. Emerton recently studied representations from viewpoint rigid geometry. In this article, we consider certain subgroups give in . particular, show existence inside prove that its non-null. This gives us a (in sense Emerton) lying