Geodesic
A complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup
Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 127-147 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that a previously known list of indecomposable spherical functions of the group $\mathrm{GL}(\infty)$ that are bilaterally invariant with respect to the unitary subgroup is complete. Bibliography: 9 titles. 
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N. I. Nessonov. A complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup. Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 127-147. http://geodesic.mathdoc.fr/item/SM_1987_58_1_a7/

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