Global Jacquet-Langlands Correspondence for Division Algebras in Characteristic p

被引：7

作者：

Badulescu, Alexandru Ioan ^{[1
]}

Roche, Philippe ^{[2
]}

机构：

[1] Univ Montpellier 2, I3M, Montpellier, France

[2] Univ Montpellier 2, CNRS, I3M, L2C, Montpellier, France

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2017年 / 2017卷 / 07期

关键词：

MULTIPLICITY ONE; GL(N); REPRESENTATIONS; THEOREM; CLASSIFICATION;

D O I：

10.1093/imrn/rnw094

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 representations of D-x 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 D-x.

引用

页码：2172 / 2206

页数：35

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