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
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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},
publisher = {mathdoc},
volume = {331},
year = {2006},
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 PB - mathdoc 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 %I mathdoc %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/