arXiv subjects

A. I. Badulescu

Publications and source records attributed to A. I. Badulescu.

4 recordsLinked to original sources

arXiv2016

Shintani relation for base change: unitary and elliptic representations

Let $E/F$ be a cyclic extension of $p$-adic fields and $n$ a positive integer. Arthur and Clozel constructed a base change process $π\mapsto π_E$ which associates to a smooth irreducible representation of $GL_n(F)$ a smooth irreducible representation of $GL_n(E)$, invariant under $Gal(E/F)$. When $π$ is tempered, $π_E$ is tempered and is characterized by an identity (the Shintani character relation) relating the character of $π$ to the character of $π_E$ twisted by the action of $Gal(E/F)$. In this paper we show that the Shintani relation also holds when $π$ is unitary or elliptic. We prove similar results for the extension $C/R$. As a corollary we show that for a cyclic extension $E/F$ of number fields the base change for automorphic residual representations of the adèle group $GL_n(A_F)$ respects the Shintani relation at each place of $F$.

math.NT↗

arXiv2014

Global Jacquet-Langlands correspondence for division algebras in characteristic p

We prove a full global Jacquet-Langlands correspondence between GL(n) and division algebras over global fields of non zero characteristic. If $D$ is a central division algebra of dimension $n^2$ over a global field $F$ of non zero characteristic, we prove that there exists an injective map from the set of automorphic square integrable representations of the multiplicative group of $D$ to the set of automorphic square integrable representations of GL_n(F), compatible at all places with the local Jacquet-Langlands correspondence for unitary representations. We characterize the image of the map. As a consequence we get multiplicity one and strong multiplicity one theorems for the multiplicative group of D.

math.NT↗

arXiv2009

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 places so that this assumption can be removed. Along the way, we collect several results about the unitary dual of general linear groups over $\bbR$, $\bbC$ or $\bbH$ of independent interest.

math.RT↗

arXiv2007

Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).

math.RT↗