On Semisimple Invariant CR Structures of Maximal Rank on the Compact Symplectic Group

We characterize semisimple invariant CR structures of maximal rank on the compact symplectic group USp 2n (C) for n = 4 .This is equivalent to characterizing complex semisimple subalgebras of maximal dimension in sp 2n (C) having trivial intersection with usp 2n (C).We conjecture that our classification remains valid for n = 4 .This extends previous results by Ounaes-Khalgui and the author for the compact groups SU n (C) and SO n (R) .