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 
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/
@article{SM_1987_58_1_a7,
     author = {N. I. Nessonov},
     title = {A~complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup},
     journal = {Sbornik. Mathematics},
     pages = {127--147},
     year = {1987},
     volume = {58},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_58_1_a7/}
}
TY  - JOUR
AU  - N. I. Nessonov
TI  - A complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup
JO  - Sbornik. Mathematics
PY  - 1987
SP  - 127
EP  - 147
VL  - 58
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1987_58_1_a7/
LA  - en
ID  - SM_1987_58_1_a7
ER  - 
%0 Journal Article
%A N. I. Nessonov
%T A complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup
%J Sbornik. Mathematics
%D 1987
%P 127-147
%V 58
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1987_58_1_a7/
%G en
%F SM_1987_58_1_a7

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

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.

[1] Gelfand I. M., Naimark M. A., “Unitarnye predstavleniya klassicheskikh grupp”, Tr. MIAN, XXXVI, 1950, 3–288 | MR | Zbl

[2] Kirillov A. A., “Predstavleniya beskonechnomernoi unitarnoi gruppy”, DAN SSSR, 212:2 (1973), 288–290 | MR | Zbl

[3] Olshanskii G. I., “Konstruktsiya unitarnykh predstavlenii beskonechnomernykh klassicheskikh grupp”, DAN SSSR, 250:2 (1980), 284–286 | MR

[4] Vershik A. M., Kerov S. V., “Kharaktery i faktor-predstavleniya beskonechnoi unitarnoi gruppy”, DAN SSSR, 267:2 (1982), 272–276 | MR | Zbl

[5] Vershik A. M., Kerov S. V., “Asimptoticheskaya teoriya kharakterov simmetricheskoi gruppy”, Funktsion. analiz i ego pril., 15:4 (1981), 15–27 | MR | Zbl

[6] Olshanskii G. I., “Unitarnye predstavleniya beskonechnomernykh par $(G,K)$ i formalizm Khau”, DAN SSSR, 269:1 (1983), 290–294 | MR

[7] Olshanskii G. I., “Unitarnye predstavleniya beskonechnomernykh klassicheskikh grupp $U(p,\infty)$, $\mathrm{SO}_0(p,\infty)$, $\mathrm{Sp}(p,\infty)$ i sootvetstvuyuschikh grupp dvizhenii”, Funktsion. analiz i ego pril., 12:3 (1978), 32–44 | MR

[8] Nessonov N. I., “Opisanie predstavlenii gruppy obratimykh operatorov gilbertova prostranstva, soderzhaschikh edinichnoe predstavlenie unitarnoi podgruppy”, Funktsion. analiz i ego pril., 17:1 (1983), 79–80 | MR | Zbl

[9] Powers R. T., “Representations of uniformly hyperfinite algebras and their associated von Neumann rings”, Ann. Math., 86 (1967), 138–171 | DOI | MR | Zbl