Geodesic
Special representations of the Borel and maximal parabolic subgroups of G 2 ( q )
Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 2 
M. Ghorbany. Special representations of the Borel and maximal parabolic subgroups of G 2 ( q ). Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2009_78_2_a7/
@article{AMUC_2009_78_2_a7,
     author = {M. Ghorbany},
     title = {Special representations of the {Borel} and maximal parabolic subgroups of {G} 2 ( q )},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2009},
     volume = {78},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2009_78_2_a7/}
}
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Voir la notice de l'article provenant de la source Comenius University

A square matrix over the complex field with a non-negative integral trace is called a quasi-permutation matrix. For a finite group G , the minimal degree of a faithful representation of G by quasi-permutation matrices over the complex numbers is denoted by c ( G ), and r ( G ) denotes the minimal degree of a faithful rational valued complex character of G . In this paper c ( G ) and r ( G ) are calculated for the Borel and maximal parabolic subgroups of G 2 ( q ).