p进幂偶群的半不变分布向量

IF 0.6 4区数学 Q3 MATHEMATICS

International Journal of Mathematics Pub Date : 2023-10-05 DOI:10.1142/s0129167x2350088x

Souha Maaref

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引用次数: 0

摘要

设[公式:见文]是定义在特征为零的[公式:见文]进域上的一个单幂代数群。我们用[公式:见文]表示[公式:见文]的有理点集。它是一个[公式:见文]-进李群，李代数表示为[公式:见文]。设[公式:见文]是希尔伯特空间[公式:见文]中[公式:见文]的不可约一元表示，[公式:见文]是[公式:见文]上的线性形式，[公式:见文]是[公式:见文]上的极化。我们用[公式:见文]表示与[公式:见文]有关的[公式:见文]的一个字符。本研究的目的是给出[公式:见文]的半不变分布向量空间[公式:见文]的精确描述。

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Semi-Invariant Distribution Vectors for P-Adic Unipotent Groups

Let [Formula: see text] be a unipotent algebraic group defined over a [Formula: see text]-adic field of characteristic zero. We denote by [Formula: see text] the set of rational points of [Formula: see text]. It is a [Formula: see text]-adic Lie group with Lie algebra denoted by [Formula: see text]. Let [Formula: see text] be an irreducible unitary representation of [Formula: see text] in a Hilbert space [Formula: see text], [Formula: see text] be a linear form on [Formula: see text] and [Formula: see text] be a polarization at [Formula: see text]. We denote by [Formula: see text] a character of [Formula: see text] related to [Formula: see text]. The aim of this study is to give a precise description of the space of semi-invariant distribution vectors [Formula: see text] of [Formula: see text].

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来源期刊

International Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： The International Journal of Mathematics publishes original papers in mathematics in general, but giving a preference to those in the areas of mathematics represented by the editorial board. The journal has been published monthly except in June and December to bring out new results without delay. Occasionally, expository papers of exceptional value may also be published. The first issue appeared in March 1990.