Geodesic
Complex representations of classical groups over a finite field
Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 135-156

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We give a description of the properties of the system of irreducible complex representations of classical groups over finite fields without using characters of representations. The description involves a multiplication of irreducible representations that generalizes the multiplication introduced by Green. More precisely, we define the concept of a prime representation and prove some results on the structure of products containing a prime representation of a classical group. 
@article{ZNSL_1979_86_a12,
     author = {S. V. Nagornyi},
     title = {Complex representations of classical groups over a finite field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--156},
     publisher = {mathdoc},
     volume = {86},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a12/}
}
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S. V. Nagornyi. Complex representations of classical groups over a finite field. Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 135-156. http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a12/