论文标题
langlands函数性猜想$ {\ bf so} _ {2n}^*$ in积极特征
Langlands functoriality conjecture for ${\bf SO}_{2n}^*$ in positive characteristic
论文作者
论文摘要
在本文中，我们关注Langlands的功能性猜想。在特征性零中，Cogdell，Kim，Piatetski-Shapiro和Shahidi证明了功能性猜想，即分裂经典群体，统一组甚至Quasi-Spplit Special Orthoconal组的全球通用性尖尖体自形表示。 Lomelí将此结果扩展到分裂的经典群体和积极特征的统一群体。因此，在本文中，我们证明了兰格兰的功能性猜想，即在积极特征的均匀分裂的非分类特殊正交组，即我们提高全球通用的cuspidal自身形式的代表，即准定的非阶段非分类的非分类非分类的非分类，甚至是特殊的矫正组，甚至是特殊的矫正型组，以使通用的一般属性属性组成的普通属性属性有特征。作为此结果的应用，我们证明了局部伽马因子的兼容性和未受到的Ramanujan猜想。
In this article, we are concerned with the Langlands functoriality conjecture. Cogdell, Kim, Piatetski-Shapiro and Shahidi proved functioriality conjecture in the case of a globally generic cuspidal automorphic representation for the split classical groups, unitary groups or even quasi-split special orthogonal groups in characteristic zero. Lomelí extends this result to split classical groups and unitary groups in positive characteristic. Thus, in this article we prove the Langlands functoriality conjecture for the even quasi-split non-split special orthogonal groups in positive characteristic i.e. we lift globally generic cuspidal automorphic representations of quasi-split non-split even special orthogonal groups to generic automorphic representations of suitable general linear groups in positive characteristic. As an application of this result, we prove the compatibility of the local gamma factors and the unramified Ramanujan conjecture.
