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).

中文翻译：

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

对于实辛群\(G=\textrm{Sp}(n,\mathbb {R})\)，我们对所有克莱因四对称对\((G,G^\Gamma )\)进行分类，并确定是否存在无限维不可约\((\mathfrak {g},K)\) -在限制为\(G^\Gamma \)的情况下可离散分解的模块。因此，我们得到了与 Chen 和 He 类似的结果（Int J Math 34(1):2250094, 2023, Corrollary 21）。