Geodesic
A~combinatorial description of the highest orbit of elementary unitary groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 226-227

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The paper gives a purely combinatorial description of the orbit of $e_1$ under the action of the elementary unitary group. 
@article{ZNSL_2003_305_a14,
     author = {V. A. Petrov},
     title = {A~combinatorial description of the highest orbit of elementary unitary groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {226--227},
     publisher = {mathdoc},
     volume = {305},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a14/}
}
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V. A. Petrov. A~combinatorial description of the highest orbit of elementary unitary groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 226-227. http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a14/