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

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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 
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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/

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