Geodesic
A normalized family of representations of the group of motions of a Euclidean space and the inverse problem of the representation theory of this group
Sbornik. Mathematics, Tome 195 (2004) no. 12, pp. 1747-1756 
R. S. Ismagilov; Sh. Sh. Sultanov. A normalized family of representations of the group of motions of a Euclidean space and the inverse problem of the representation theory of this group. Sbornik. Mathematics, Tome 195 (2004) no. 12, pp. 1747-1756. http://geodesic.mathdoc.fr/item/SM_2004_195_12_a2/
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     title = {A~normalized family of representations of the group of motions of {a~Euclidean} space and the inverse problem of the representation theory of this group},
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Voir la notice de l'article provenant de la source Math-Net.Ru

There exists a well-known holomorphic family $\mathscr T^\lambda$ of representations of the isometry group of $\mathbb R$ such that $\mathscr T^{-\lambda}\sim\mathscr T^\lambda$ for $\lambda\ne0$. This paper presents a holomorphic family $V_R^{\lambda}$, $|\lambda|, such that $V_R^\lambda\sim\mathscr T^\lambda$ and $V_R^{-\lambda}= V_R^\lambda$ for $\lambda\ne0$. It is used for the construction of (generally speaking, reducible) representations of a fairly general form.

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