Theta correspondence and simple factors in global Arthur parameters

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2024-04-16 DOI:10.2140/ant.2024.18.969

Chenyan Wu

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引用次数: 0

Abstract

By using results on poles of $L$ -functions and theta correspondence, we give a bound on $b$ for $(χ, b)$ -factors of the global Arthur parameter of a cuspidal automorphic representation $π$ of a classical group or a metaplectic group where $χ$ is a conjugate self-dual automorphic character and $b$ is an integer which is the dimension of an irreducible representation of ${SL}_{2} (ℂ)$ . We derive a more precise relation when $π$ lies in a generic global $A$ -packet.

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全局阿瑟参数中的 Theta 对应和简单因子

通过利用 L 函数极点和 Theta 对应的结果，我们给出了经典群或偏正群的尖顶自形表示 π 的全局阿瑟参数 (χ,b)- 因子的 b 约束，其中 χ 是共轭自偶自形特征，b 是一个整数，即 SL 2(ℂ) 不可还原表示的维数。当 π 位于一般全局 A 包中时，我们会推导出更精确的关系。

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.