Geodesic
The simplicity of branching of the principal series representations of the groups $GL(n,q)$ under the parabolic restrictions
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Tome 331 (2006), pp. 43-59 
E. E. Goryachko. The simplicity of branching of the principal series representations of the groups $GL(n,q)$ under the parabolic restrictions. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Tome 331 (2006), pp. 43-59. http://geodesic.mathdoc.fr/item/ZNSL_2006_331_a4/
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     author = {E. E. Goryachko},
     title = {The simplicity of branching of the principal series representations of the groups $GL(n,q)$ under the parabolic restrictions},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider the parabolic restriction of representations of the group $GL(n+1,q)$ to the group $GL(n,q)$. The branching of representations under this restriction is simple. We present a direct proof of this fact in the case of the so-called principal series representations. This statement is reduced to the commutativity of the centralizer of the Hecke algebras $Z(H(n,q),H(n+1,q))$; we prove it using an auxiliary combinatorial theory.

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