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@article{FAA_2014_48_3_a0, author = {A. M. Vershik and M. I. Graev}, title = {Cohomology in {Nonunitary} {Representations} of {Semisimple} {Lie} {Groups} (the {Group} $U(2,2)$)}, journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a}, pages = {1--13}, publisher = {mathdoc}, volume = {48}, number = {3}, year = {2014}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a0/} }
TY - JOUR AU - A. M. Vershik AU - M. I. Graev TI - Cohomology in Nonunitary Representations of Semisimple Lie Groups (the Group $U(2,2)$) JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 2014 SP - 1 EP - 13 VL - 48 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a0/ LA - ru ID - FAA_2014_48_3_a0 ER -
A. M. Vershik; M. I. Graev. Cohomology in Nonunitary Representations of Semisimple Lie Groups (the Group $U(2,2)$). Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 3, pp. 1-13. http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a0/
[1] A. M. Vershik, S. I. Karpushev, “Kogomologii grupp v unitarnykh predstavleniyakh, okrestnost edinitsy i uslovno polozhitelno opredelennye funktsii”, Matem. sb., 119:4 (1982), 521–533 | MR | Zbl
[2] Y. Shalom, “Rigidity of commensurators and irreducible lattices”, Invent. Math., 141:1 (2000), 1–54 | DOI | MR | Zbl
[3] B. Bekka, P. de la Harpe, A. Valette, Kazdan's Property (T), Cambridge University Press, Cambridge, 2007 | MR
[4] U. Haagrup, “An example of nonnuclear $C^*$-algebra, which has the metric approximation property”, Invent. Math., 50:3 (1978), 279–293 | DOI | MR
[5] P-A. Cherix, et al., Groups with the Haagerup Property: Gromov's A-T-Menability, Birkhäuser Verlag, Basel, 2001 | MR
[6] B. Kostant, “On existence and irreducibility of certain series of representations”, Bull. Amer. Math Soc., 75 (1969), 627–642 | DOI | MR | Zbl
[7] A. M. Vershik, I. M. Gelfand, M. I. Graev, “Predstavleniya gruppy $SL(2,R)$, gde $R$ — koltso funktsii”, UMN, 28:5(173) (1973), 83–128 | MR
[8] A. M. Vershik, I. M. Gelfand, M. I. Graev, “Neprivodimye predstavleniya gruppy $G^X$ i kogomologii”, Funkts. analiz i ego pril., 8:2 (1974), 67–69 | MR | Zbl
[9] I. M. Gelfand, M. I. Graev, A. M. Vershik, “Models of representations of current groups”, Representations of Lie groups and Lie algebras (Budapest, 1971), Akad. Kiadó, Budapest, 1985, 121–179 | MR
[10] R. S. Ismagilov, Representations of infinite-dimensional groups, Transl. Math. Monographs, 152, Amer. Math. Soc., Providence, RI, 1996 | DOI | MR | Zbl
[11] A. Guichardet, “Sur la cohomologie des groupe topologiques II”, Bull. Soc. Math. France, 96 (1972), 305–332 | MR | Zbl
[12] P. Delorm, “$1$-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubes. Produits tenoriels continus et représentations”, Bull. Soc. Math. France, 105 (1977), 281–336 | DOI | MR | Zbl
[13] F. A. Berezin, “Predstavleniya nepreryvnogo pryamogo proizvedeniya universalnykh nakryvayuschikh gruppy dvizhenii kompleksnogo shara”, Trudy MMO, 36 (1978), 275–293 | MR | Zbl
[14] H. Araki, “Factorisable representations of current algebra”, Publ. Res. Inst. Math. Sci., Kyoto Univ., Ser. A, 5 (1969/1970), 361–422 | DOI | MR
[15] K. Parthasarathi, K. Schmidt, Positive Definite Kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory, Springer-Verlag, Berlin–New York, 1972 | MR
[16] A. M. Vershik, M. I. Graev, “The basic representation of the current group $O(n,1)^X$ in the $L^2$ space over the generalized Lebesgue measure”, Indag. Math., 16:3/4 (2005), 499–529 | MR | Zbl
[17] A. M. Vershik, M. I. Graev, “Struktura dopolnitelnykh serii i osobykh predstavlenii grupp $SO(n,1)$ i $SU(n,1)$”, UMN, 61:5 (2006), 3–88 | DOI | MR | Zbl
[18] A. M. Vershik, M. I. Graev, “Integralnye modeli predstavlenii grupp tokov”, Funkts. analiz i ego pril., 42:1 (2008), 22–32 | DOI | MR | Zbl
[19] A. M. Vershik, M. I. Graev, “Integralnye modeli predstavlenii grupp tokov prostykh grupp Li”, UMN, 64:2(386) (2009), 5–72 | DOI | MR | Zbl
[20] A. M. Vershik, M. I. Graev, “Puassonova model fokovskogo prostranstva i predstavleniya grupp tokov”, Algebra i analiz, 23:3 (2011), 63–136 | MR
[21] A. M. Vershik, M. I. Graev, “Osobye predstavleniya grupp $U(n,1)$ i $O(n,1)$ i svyazannye s nimi predstavleniya grupp tokov $U(\infty,1)$ i $O(\infty,1)$ v kvazipuassonovom prostranstve”, Funkts. analiz i ego pril., 46:1 (2012), 1–12 | DOI | MR | Zbl
[22] A. M. Vershik, “Suschestvuet li mera Lebega v beskonechnomernom prostranstve?”, Trudy MIAN, 259 (2007), 256–281 | MR | Zbl
[23] A. M. Vershik, “Invariant measures for the continual Cartan subgroup”, J. Funct. Anal., 255:9 (2008), 2661–2682 | DOI | MR | Zbl
[24] A. M. Vershik, “The behavior of the Laplace transform of the invariant measure on the hypersphere of high dimension”, J. Fixed Point Theory Appl., 3:2 (2008), 317–329 | DOI | MR | Zbl
[25] E. B. Vinberg, A. L. Onischik, Ceminar po gruppam Li i algebraicheskim gruppam, Nauka, M, 1988 | MR