-indistinguishability and -groups for quasisplit groups : unitary groups in even dimension
We prove the compatibility of the local and global Langlands correspondences at places dividing for the -adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing and have Shin-regular weight.
The -adic local Langlands correspondence for attaches to any -dimensional irreducible -adic representation of an admissible unitary representation of . The unitary principal series of are those corresponding to trianguline representations. In this article, for , using the machinery of Colmez, we determine the space of locally analytic vectors for all non-exceptional unitary principal series of by proving a conjecture of Emerton.