Fourier-Poisson Transforms Associated with the Principal Series Representations of Sp(1, n)

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-28 DOI:10.1007/s00006-024-01330-1

Xingya Fan, Jianxun He, Xiaoke Jia

引用次数: 0

Abstract

Let \(X=Sp(1,n)/Sp(n)\) be the quaternion hyperbolic space with a left invariant Haar measure, unique up to scalars, where n is greater than or equal to 1. The Fürstenberg boundary of X is denoted as \(\Sigma \). In this paper, we focus on the Plancherel formula on X associated with the Poisson transform of vector-valued \(L^2\)-space on \(\Sigma \). Through the Fourier-Jacobi transform and the Fourier-Poisson transform, we derive the Plancherel decomposition of the unitary representation of Sp(1, n) on \(L^2(X)\).

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与 Sp(1, n) 主数列表示相关的傅立叶-泊松变换

让（X=Sp(1,n)/Sp(n)\）是具有左不变哈量的四元双曲空间，对标量是唯一的，其中 n 大于或等于 1，X 的 Fürstenberg 边界表示为（\Sigma \）。在本文中，我们将重点研究与 \(\Sigma\) 上的矢量值 \(L^2\)-space 的泊松变换相关的 X 上的 Plancherel 公式。通过傅里叶-雅可比变换和傅里叶-泊松变换，我们得出了 Sp(1, n) 在 \(L^2(X)\) 上的单元表示的 Plancherel 分解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.