Journal of Lie Theory 33 (2023), No. 4, 1009--1024
Copyright Heldermann Verlag 2023
On Semisimple Invariant CR Structures of Maximal Rank on the Compact Symplectic Group
Rupert W. T. Yu
Lab. de Mathématiques de Reims UMR 9008 CNRS, Université de Reims Champagne-Ardenne, Reims, France
rupert.yu@univ-reims.fr
[Abstract-pdf]
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 $\mathrm{SO}_{n}(\mathbb{R})$.
Keywords: Compact Lie group, CR structure, representations of simple Lie algebras.
MSC: 17B10, 22E99, 32V05.
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