Branching laws of Klein four-symmetric pairs for $$\textrm{Sp}(n,\mathbb {R})$$

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2024-04-11 DOI:10.1007/s10711-024-00922-2

Jiaying Ding, Haian He, Huangyuan Pan, Lifu Wang

引用次数: 0

Abstract

For the real symplectic groups $G=\textrm{Sp}(n,\mathbb {R})$, we classify all the Klein four-symmetric pairs $(G,G^\Gamma )$, and determine whether there exist infinite-dimensional irreducible $(\mathfrak {g},K)$-modules discretely decomposable upon restriction to $G^\Gamma $. As a consequence, we obtain a similar result to Chen and He (Int J Math 34(1):2250094, 2023, Corollary 21).

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$$textrm{Sp}(n,\mathbb {R})$$ 的克莱因四对称对的分支规律

对于实交点群 $G=\textrm{Sp}(n,\mathbb {R})$，我们对所有克莱因四对称对 $(G,G^\Gamma )$进行了分类，并确定了是否存在限制于 $G^\Gamma$时可离散分解的无限维不可还原 $(\mathfrak {g},K)$- 模块。因此，我们得到了与 Chen 和 He (Int J Math 34(1):2250094, 2023, Corollary 21) 类似的结果。

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

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.