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

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).