仿射对称空间 $SO^\ast(6)/SO(3,\mathbb{C})$ 上的离散序列

数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1649-1658.

仿射对称空间 $SO^\ast(6)/SO(3,\mathbb{C})$ 上的离散序列

兰超(),范兴亚^*()

新疆大学数学与系统科学学院乌鲁木齐 830017

收稿日期:2022-04-09 修回日期:2023-05-15 出版日期:2023-12-26 发布日期:2023-11-16
通讯作者: *范兴亚，E-mail: fanxingya@xju.edu.cn
作者简介:兰超，E-mail: lc_@stu.xju.edu.cn
基金资助:
国家自然科学基金(12161083);国家自然科学基金(12126360);新疆自然科学基金(2020D01C048);新疆自然科学基金(2021D01C071)

The Discrete Series of Affine Symmetric Space ${SO^\ast(6)/SO(3,\mathbb{C})}$

Lan Chao(),Fan Xingya^*()

College of Mathematics and System Science, Xinjiang University, Urumqi 830017

Received:2022-04-09 Revised:2023-05-15 Online:2023-12-26 Published:2023-11-16
Supported by:
NSFC(12161083);NSFC(12126360);Natural Science Foundation of Xinjiang Uygur Autonomous Region(2020D01C048);Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01C071)

摘要/Abstract

摘要：

该文通过 Hermite 型仿射对称空间的局部同构, 得到了 $SO^\ast(6)/SO(3,\mathbb{C})$ 的部分离散序列, 并给出来了循环向量生成的全纯离散序列的具体形式.

关键词: Hermite 型仿射对称空间, 离散序列, Bergman 空间

Abstract:

In this paper, the partial discrete sequence of $SO^\ast(6)/SO(3,\mathbb{C})$ is obtained by local isomorphism of Hermite-type affine symmetric space, and the specific form of the holomorphic discrete sequence generated by the cyclic vector is given.

Key words: Affine symmetric space of Hermitian type, Discrete series, Bergman space

中图分类号:

O152.5

兰超, 范兴亚. 仿射对称空间 $SO^\ast(6)/SO(3,\mathbb{C})$ 上的离散序列[J]. 数学物理学报, 2023, 43(6): 1649-1658.

Lan Chao, Fan Xingya. The Discrete Series of Affine Symmetric Space ${SO^\ast(6)/SO(3,\mathbb{C})}$[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1649-1658.

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