Local Shimura Correspondence.
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.
It is proven that an infinite-dimensional Banach space (considered as an Abelian topological group) is not topologically isomorphic to a subgroup of a product of -compact (or more generally, -bounded) topological groups. This answers a question of M. Tkachenko.
Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topological lattice-ordered groups. In particular, we show that a group topology on a lattice-ordered group is...
Given idempotents e and f in a semigroup, e ≤ f if and only if e = fe = ef. We show that if G is a countable discrete group, p is a right cancelable element of G* = βG∖G, and λ is a countable ordinal, then there is a strictly decreasing chain of idempotents in , the smallest compact subsemigroup of G* with p as a member. We also show that if S is any infinite subsemigroup of a countable group, then any nonminimal idempotent in S* is the largest element of such a strictly decreasing chain of idempotents....