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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{ZNSL_2006_331_a4,
     author = {E. E. Goryachko},
     title = {The simplicity of branching of the principal series representations of the groups $GL(n,q)$ under the parabolic restrictions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {43--59},
     year = {2006},
     volume = {331},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_331_a4/}
}
TY  - JOUR
AU  - E. E. Goryachko
TI  - The simplicity of branching of the principal series representations of the groups $GL(n,q)$ under the parabolic restrictions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 43
EP  - 59
VL  - 331
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_331_a4/
LA  - ru
ID  - ZNSL_2006_331_a4
ER  - 
%0 Journal Article
%A E. E. Goryachko
%T The simplicity of branching of the principal series representations of the groups $GL(n,q)$ under the parabolic restrictions
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 43-59
%V 331
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_331_a4/
%G ru
%F ZNSL_2006_331_a4
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/

[1] A. M. Vershik, S. V. Kerov, “Ob odnoi beskonechnomernoi gruppe nad konechnym polem”, Funkts. anal. i ego pril., 32:3 (1998), 3–10 | MR | Zbl

[2] A. M. Vershik, A. Yu. Okunkov, “Novyi podkhod k teorii predstavlenii simmetricheskikh grupp, II”, Zap. nauchn. semin. POMI, 307, 2004, 57–98 | MR

[3] I. M. Gelfand, “Sfericheskie funktsii na simmetricheskikh rimanovykh prostranstvakh”, Dokl. Akad. Nauk SSSR, 70:1 (1950), 5–8

[4] S. I. Gelfand, “Predstavleniya polnoi lineinoi gruppy nad konechnym polem”, Mat. sb., 83:1 (1970), 15–41

[5] D. K. Faddeev, “Kompleksnye predstavleniya polnoi lineinoi gruppy nad konechnym polem”, Zap. nauch. semin. LOMI, 46, 1974, 64–88 | MR | Zbl

[6] J. A. Green, “The characters of the finite general linear groups”, Trans. Amer. Math. Soc., 80:2 (1955), 402–447 | DOI | MR | Zbl

[7] N. Iwahori, “On the structure of a Hecke ring of a Chevalley group over a finite field”, J. Fac. Sci. Univ. Tokyo. Sec. I, 10 (1964), 215–236 | MR | Zbl

[8] L. Solomon, “The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field”, Geom. Dedic., 36:1 (1990), 15–49 | DOI | MR | Zbl

[9] A. Zelevinsky, Representations of Finite Classical Groups. A Hopf Algebra Approach, Lect. Notes in Math., 869, 1981 | MR | Zbl