非阿基米德局部域上一般线性群的局部新形式

IF 2.8 1区数学 Q1 MATHEMATICS

Forum of Mathematics Pi Pub Date : 2021-10-18 DOI:10.1017/fmp.2022.17

Hiraku Atobe, S. Kondo, S. Yasuda

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引用次数: 8

摘要

在[14]中，Jacquet–Piatetskii Shapiro–Shalika定义了由非负整数索引的p-adic广义线性群的紧致开子群族，并建立了不可约泛型表示的局部新形式理论。在本文中，我们将它们的结果推广到所有不可约表示。为此，我们定义了一个由非负整数的某些元组索引的紧致开子群的新族。为了证明，我们引入了Speh表示的Rankin–Selberg积分。

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Local newforms for the general linear groups over a non-archimedean local field

In [14], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups of p-adic general linear groups indexed by nonnegative integers and established the theory of local newforms for irreducible generic representations. In this paper, we extend their results to all irreducible representations. To do this, we define a new family of compact open subgroups indexed by certain tuples of nonnegative integers. For the proof, we introduce the Rankin–Selberg integrals for Speh representations.

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来源期刊

Forum of Mathematics Pi Mathematics-Statistics and Probability

CiteScore

3.50

自引率

0.00%

发文量

审稿时长

19 weeks

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