Some Endoscopic Properties of The Essentially Tame Jacquet-Langlands Correspondence

Supercuspidal Representations: an Exhaustion Theorem

Let k be a p-adic field of characteristic zero and residue characteristic p. Let G be the group of k-points of a connected reductive group G defined over k. In [38], Yu gives a fairly general construction of supercuspidal representations of G in a certain tame situation. In this paper, subject to some hypotheses on G and k, we prove that all supercuspidal representations arise through his const...

8 On a p - adic extension of the Jacquet - Langlands correspondence to weight 1

In this paper, we consider a novel version of the classical Jacquet-Langlands correspondence, explore a p-adic extension of the correspondence , and as an explicit example we find an overconvergent automorphic form of weight 1 which corresponds to a classical modular form of weight 1, using both experimental and theoretical methods.

ON REPRESENTATION THEORY OF GL(n) OVER p-ADIC DIVISION ALGEBRA AND UNITARITY IN JACQUET-LANGLANDS CORRESPONDENCE

Let F be a p-adic field of characteristic 0, and let A be an F -central division algebra of dimension dA over F . In the paper we first develop the representation theory of GL(m,A), assuming that holds the conjecture which claims that unitary parabolic induction is irreducible for GL(m,A)’s. Among others, we obtain the formula for characters of irreducible unitary representations of GL(m,A) in ...

The Jacquet-Langlands correspondence via `-adic uniformization

UNITARY DUAL OF GL(n) AT ARCHIMEDEAN PLACES AND GLOBAL JACQUET-LANGLANDS CORRESPONDENCE

In [7], results about the global Jacquet-Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field are established, under the condition that the local inner forms are split at archimedean places. In this paper, we extend the main local results of [7] to archimedean p...