Journal of Lie Theory

no. 4
On Semisimple Invariant CR Structures of Maximal Rank on the Compact Symplectic Group
Journal of Lie Theory, Volume 33 (2023) no. 4, pp. 1009-1024
We characterize semisimple invariant {\it CR} structures of maximal rank on the compact symplectic group $\mathrm{USp}_{2n}(\mathbb{C})$ for $n\neq 4$. This is equivalent to characterizing complex semisimple subalgebras of maximal dimension in $\mathrm{sp}_{2n}(\mathbb{C})$ having trivial intersection with $\mathrm{usp}_{2n}(\mathbb{C})$. We conjecture that our classification remains valid for $n=4$. This extends previous results by Ouna\"\i es-Khalgui and the author for the compact groups $\mathrm{SU}_{n}(\mathbb{C})$ and $\mathrm{SO}_{n}(\mathbb{R})$.
DOI: 10.5802/jolt.1317
Classification: 17B10, 22E99, 32V05
Keywords: Compact Lie group, CR structure, representations of simple Lie algebras 
@article{JOLT_2023_33_4_a3,
     author = {R. W. T. Yu},
     title = {On {Semisimple} {Invariant} {CR} {Structures} of {Maximal} {Rank} on the {Compact} {Symplectic} {Group}},
     journal = {Journal of Lie Theory},
     pages = {1009--1024},
     year = {2023},
     volume = {33},
     number = {4},
     doi = {10.5802/jolt.1317},
     zbl = {1544.17030},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1317/}
}
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R. W. T. Yu. On Semisimple Invariant CR Structures of Maximal Rank on the Compact Symplectic Group. Journal of Lie Theory, Volume 33 (2023) no. 4, pp. 1009-1024. doi: 10.5802/jolt.1317

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