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

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras 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

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.