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

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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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Funding

Haian HE is supported by Natural Science Foundation of Shanghai (Grant Number 22ZR1422900).

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, China

    Jiaying Ding, Haian He, Huangyuan Pan & Lifu Wang

  2. Newtouch Center for Mathematics of Shanghai University, Shanghai, 200444, China

    Haian He

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  1. Jiaying Ding
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  2. Haian He
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  3. Huangyuan Pan
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  4. Lifu Wang
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Haian HE wrote the main manuscript text and other authors helped to check the computation. All authors reviewed the manuscript.

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Correspondence to Haian He.

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Ding, J., He, H., Pan, H. et al. Branching laws of Klein four-symmetric pairs for \(\textrm{Sp}(n,\mathbb {R})\). Geom Dedicata 218, 69 (2024). https://doi.org/10.1007/s10711-024-00922-2

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