对偶对(U(1),U(1,n))意义下的辛表示及其不可约分解

代金刚; 范兴亚

doi:10.13568/j.cnki.651094.651316.2023.10.20.0001

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对偶对(U(1),U(1,n))意义下的辛表示及其不可约分解

更新时间：2026-01-21

- 对偶对(U(1),U(1,n))意义下的辛表示及其不可约分解
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 41, Issue 3, Pages: 279-287(2024)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2023.10.20.0001
  CLC： O152.5
- Published：2024
- 稿件说明：
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[1]代金刚,范兴亚.对偶对(U(1),U(1,n))意义下的辛表示及其不可约分解[J].新疆大学学报(自然科学版)(中英文),2024,41(03):279-287.
[1]代金刚,范兴亚.对偶对(U(1),U(1,n))意义下的辛表示及其不可约分解[J].新疆大学学报(自然科学版)(中英文),2024,41(03):279-287. DOI： 10.13568/j.cnki.651094.651316.2023.10.20.0001.

DOI：10.13568/j.cnki.651094.651316.2023.10.20.0001.

摘要

考虑了对偶对(U(1)

U(1

n))下的辛表示的不可约分解问题.主要的想法是构造两个李群SL(2

R)和U(1

n)表示的缠结算子

将对应的表示空间分解为不可约SL(2

R)×U(1

n)-模.以Fourier-Poisson变换作为主要工具

并结合此变换的Plancherel公式

得到了辛表示的谱分解.

Abstract

We considered the problem of irreducible decomposition of the symplectic representation under the dual pair(U(1)

U(1

n)). The main idea is to construct the intertwining operator of representation of SL(2

R)and U(1

and the corresponding representation space is decomposed into irreducible SL(2

R)×U(1

n)-module.The main technique used in this paper is the Fourier-Poisson transform

combining the Plancherel formula of this transform

we obtain the spectrum of the symplectic representation.

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references

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