Geodesic
Tensor Products as Induced Representations: The Case of Finite $\mathrm{GL}(3)$
Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 483-494

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe the tensor products of two irreducible linear complex representations of the group $G=\mathrm{GL}(3,\mathbb F_q)$ in terms of induced representations by linear characters of maximal tori and also in terms of Gelfand–Graev representations. Our results include MacDonald's conjectures for $G$ and are extensions to $G$ of finite counterparts to classical results on tensor products of principal series as well as holomorphic and antiholomorphic representations of the group $\mathrm{SL}(2,\mathbb R)$; besides, they provide an easy way to decompose these tensor products with the help of Frobenius reciprocity. We also state some conjectures for the general case of $\mathrm{GL}(n,\mathbb F_q)$.
Keywords: tensor products decomposition, irreducible representation of the general linear groups over finite fields, induced representations.
Mots-clés : Clebsch–Gordan coefficients 
@article{MZM_2012_91_4_a0,
     author = {L. Aburto-Hageman and J. Pantoja and J. Soto-Andrade},
     title = {Tensor {Products} as {Induced} {Representations:} {The} {Case} of {Finite} $\mathrm{GL}(3)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--494},
     publisher = {mathdoc},
     volume = {91},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a0/}
}
TY  - JOUR
AU  - L. Aburto-Hageman
AU  - J. Pantoja
AU  - J. Soto-Andrade
TI  - Tensor Products as Induced Representations: The Case of Finite $\mathrm{GL}(3)$
JO  - Matematičeskie zametki
PY  - 2012
SP  - 483
EP  - 494
VL  - 91
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a0/
LA  - ru
ID  - MZM_2012_91_4_a0
ER  - 
%0 Journal Article
%A L. Aburto-Hageman
%A J. Pantoja
%A J. Soto-Andrade
%T Tensor Products as Induced Representations: The Case of Finite $\mathrm{GL}(3)$
%J Matematičeskie zametki
%D 2012
%P 483-494
%V 91
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a0/
%G ru
%F MZM_2012_91_4_a0
L. Aburto-Hageman; J. Pantoja; J. Soto-Andrade. Tensor Products as Induced Representations: The Case of Finite $\mathrm{GL}(3)$. Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 483-494. http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a0/