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 
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/
@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},
     year = {2003},
     volume = {305},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a14/}
}
TY  - JOUR
AU  - V. A. Petrov
TI  - A combinatorial description of the highest orbit of elementary unitary groups
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 226
EP  - 227
VL  - 305
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a14/
LA  - ru
ID  - ZNSL_2003_305_a14
ER  - 
%0 Journal Article
%A V. A. Petrov
%T A combinatorial description of the highest orbit of elementary unitary groups
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 226-227
%V 305
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a14/
%G ru
%F ZNSL_2003_305_a14

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper gives a purely combinatorial description of the orbit of $e_1$ under the action of the elementary unitary group.

[1] V. A. Petrov, “Nechetnye unitarnye gruppy”, Zap. nauchn. semin. POMI, 305, 2003, 195–225 | MR

[2] E. K. Hinson, “Paths of unimodular vectors”, J. Algebra, 142 (1991), 58–75 | DOI | MR | Zbl

[3] E. K. Hinson, “Word length in elementary matrices”, J. Algebra, 142 (1991), 76–80 | DOI | MR | Zbl