Voir la notice de l'article provenant de la source Math-Net.Ru
@article{FAA_1984_18_1_a4, author = {G. I. Olshanskii}, title = {Infinite-dimensional classical groups of finite $r$-rank: {Description} of representations and asymptotic theory}, journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a}, pages = {28--42}, publisher = {mathdoc}, volume = {18}, number = {1}, year = {1984}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FAA_1984_18_1_a4/} }
TY - JOUR AU - G. I. Olshanskii TI - Infinite-dimensional classical groups of finite $r$-rank: Description of representations and asymptotic theory JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 1984 SP - 28 EP - 42 VL - 18 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_1984_18_1_a4/ LA - ru ID - FAA_1984_18_1_a4 ER -
%0 Journal Article %A G. I. Olshanskii %T Infinite-dimensional classical groups of finite $r$-rank: Description of representations and asymptotic theory %J Funkcionalʹnyj analiz i ego priloženiâ %D 1984 %P 28-42 %V 18 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/FAA_1984_18_1_a4/ %G ru %F FAA_1984_18_1_a4
G. I. Olshanskii. Infinite-dimensional classical groups of finite $r$-rank: Description of representations and asymptotic theory. Funkcionalʹnyj analiz i ego priloženiâ, Tome 18 (1984) no. 1, pp. 28-42. http://geodesic.mathdoc.fr/item/FAA_1984_18_1_a4/
[1] Kirillov A.A., “Predstavleniya beskonechnomernoi unitarnoi gruppy”, DAN SSSR, 212:2 (1973), 288–290 | MR | Zbl
[2] Olshanskii G.I., “Unitarnye predstavleniya beskonechnomernykh klassicheskikh grupp $U(p,\infty)$, $SO_0(p,\infty)$, $Sp(p,\infty)$ i sootvetstvuyuschikh grupp dvizhenii”, Funkts. analiz, 12:3 (1978), 32–44 | MR
[3] Olshanskii G.I., “Opisanie unitarnykh predstavlenii so starshim vesom dlya grupp $U(p,q)\widetilde{\hphantom{H}}$”, Funkts. analiz, 14:3 (1980), 32–44 | MR
[4] Olshanskii G.I., “Invariantnye konusy v algebrakh Li, polugruppy Li i golomorfnaya diskretnaya seriya”, Funkts. analiz, 15:4 (1981), 53–66 | MR
[5] Olshanskii G.I., “Unitarnye predstavleniya beskonechnomernykh klassicheskikh grupp $U(p,\infty)$, $SO_0(p,\infty)$, $Sp(p,\infty)$ i sootvetstvuyuschikh grupp dvizhenii”, DAN SSSR, 238:6 (1978), 1295–1298 | MR
[6] Olshanskii G.I., “Konstruktsiya unitarnykh predstavlenii beskonechnomernykh klassicheskikh grupp”, DAN SSSR, 250:2 (1980), 284–288 | MR
[7] Olshanskii G.I., “Invariantnye uporyadocheniya v prostykh gruppakh Li: reshenie zadachi E.B. Vinberga”, Funkts. analiz, 16:4 (1982), 80–81 | MR
[8] Olshanskii G.I., “Vypuklye konusy v simmetricheskikh algebrakh Li, polugruppy Li i invariantnye prichinnye struktury (uporyadocheniya) na psevdorimanovykh simmetricheskikh prostranstvakh”, DAN SSSR, 265:3 (1982), 537–541 | MR
[9] Olshanskii G.I., “Kompleksnye polugruppy Li, obobschennye prostranstva Khardi i programma Gelfanda–Gindikina”, Voprosy teorii grupp i gomologicheskoi algebry, Izd. Yarosl. un-ta, Yaroslavl, 1982, 85–98 | MR
[10] Olshanskii G.I., “Unitarnye predstavleniya beskonechnomernykh klassicheskikh grupp i formalizm R. Khau”, DAN SSSR, 269:1 (1983), 33–36 | MR
[11] Vershik A.M., Kerov S.V., “Asimptoticheskaya teoriya kharakterov simmetricheskoi gruppy”, Funkts. analiz, 15:4 (1981), 15–27 | MR | Zbl
[12] Vershik A.M., Kerov S.V., “Kharaktery i faktor-predstavleniya beskonechnoi unitarnoi gruppy”, DAN SSSR, 267:2 (1982), 272–276 | MR | Zbl
[13] Kolomytsev V.I., Samoilenko Yu.S., “O neprivodimykh predstavleniyakh induktivnykh predelov grupp”, Ukr. matem. zh., 29 (1977), 526–531 | MR | Zbl
[14] Zhelobenko D.P., Kompaktnye gruppy Li i ikh predstavleniya, Nauka, M., 1970 | MR | Zbl
[15] Diksme Zh., $C^*$-algebry i ikh predstavleniya, Nauka, M., 1974 | MR
[16] Lüscher M., Mack G., “Global conformal invariance in quantum field theory”, Comm. Math. Phys., 41 (1975), 203–234 | DOI | MR
[17] Nelson E., “Analytic vectors”, Ann. Math., 70 (1959), 572–615 | DOI | MR | Zbl
[18] Hida T., Nomoto H., “Gaussian measure on the projective limit space of spheres”, Proc. Japan Acad., 40 (1964), 301–304 | DOI | MR | Zbl
[19] Yamasaki Y., “Kolmogorov's extension theorem for infinite measure”, Publ. Res. Inst. Math. Sci. Kyoto Univ., 10 (1975), 381–411 | DOI | MR | Zbl
[20] Matsushima H., Okamoto K., Sakurai T., “On a certain class of irreducible unitary representations of the infinite-dimensional rotational group”, Hiroshima Math. J., 11 (1981), 181–192 | DOI | MR
[21] Schlichtkrull H., “A series of unitary irreducible representations induced from a symmetric subgroup of a semi-simple Lie group”, Invent. Math., 68 (1982), 497–516 | DOI | MR | Zbl