Mathematical works of D. P. Zhelobenko

Yu. A. Neretin   ; S. M. Khoroshkin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 64 (2009) no. 1, pp. 187-198

Bibliographie

[1] R. M. Asherova, Yu. F. Smirnov, V. N. Tolstoi, “Projection operators for simple Lie groups”, Theoret. and Math. Phys., 8:2 (1971), 813–825 | DOI | MR | Zbl

[2] R. M. Asherova, Yu. F. Smirnov, B. N. Tolstoi, “Projection operators for simple Lie groups. II. General scheme for constructing lowering operators. The groups $SU(n)$”, Theoret. and Math. Phys., 15:1 (1973), 392–401 | DOI | MR | Zbl

[3] G. E. Baird, L. C. Biedenharn, “On representations of the semisimple Lie groups. II”, J. Math. Phys., 4 (1963), 1449–1466 | DOI | MR

[4] A. Beilinson, J. Bernstein, “Localisation de $g$-modules”, C. R. Acad. Sci. Paris Sér. I Math., 292:1 (1981), 15–18 | MR | Zbl

[5] F. A. Berezin, “Operatory Laplasa na poluprostykh gruppakh”, Dokl. AN SSSR, 107 (1956), 9–12 | MR | Zbl

[6] F. A. Berezin, “Operatory Laplasa na poluprostykh gruppakh”, Tr. MMO, 6, 1957, 371–463 | MR | Zbl

[7] J. Bernstein, I. Gelfand, S. Gelfand, “Structure locale de la catégorie des modules de Harish-Chandra”, C. R. Acad. Sci. Paris Sér. A–B, 286:11 (1978), A495–A497 | MR | Zbl

[8] A. Borel, N. R. Wallach, Continuous cohomologies, discrete subgroups, and representations of reductive groups, Ann. of Math. Stud., 94, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1980 | MR | Zbl

[9] F. Bruhat, “Sur les représentations induites des groupes de Lie”, Bull. Soc. Math. France, 84 (1956), 97–205 | MR | Zbl

[10] J.-L. Brylinski, M. Kashiwara, “Kazhdan–Lusztig conjecture and holonomic systems”, Invent. Math., 64:3 (1981), 387–410 | DOI | MR | Zbl

[11] W. Casselman, The differential equations satisfied by matrix coefficients, Unpublished manuscript, 1975

[12] W. Casselman, D. Miličić, “Asymptotic behavior of matrix coefficients of admissible representations”, Duke Math. J., 49:4 (1982), 869–930 | DOI | MR | Zbl

[13] J. Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, 37, Gauthier-Villars, Paris–Brussels–Montreal, QC, 1974 | MR | Zbl

[14] M. Duflo, “Représentations irréductibles des groupes semi-simples complexes”, Analyse harmonique sur les groupes de Lie (Nancy–Strasbourg, 1973–75), Lecture Notes in Math., 497, Springer, Berlin, 1975, 26–88 | DOI | MR | Zbl

[15] P. Etingof, A. Varchenko, “Dynamical Weyl groups and applications”, Adv. Math., 167:1 (2002), 74–127 | DOI | MR | Zbl

[16] G. Felder, “Conformal field theory and integrable systems associated with elliptic curves”, Proceedings of the International Congress of Mathematicians, Vols. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, 1247–1255 | MR | Zbl

[17] M. Flensted-Jensen, “Discrete series for semisimple symmetric spaces”, Ann. of Math. (2), 111:2 (1980), 253–311 | DOI | MR | Zbl

[18] I. M. Gelfand, M. A. Naimark, Unitarnye predstavleniya klassicheskikh grupp, Tr. MIAN, 36, Izd-vo AN SSSR, M.–L., 1950 | MR | Zbl

[19] I. M. Gel'fand, V. A. Ponomarev, “Indecomposable representations of the Lorentz group”, Russian Math. Surveys, 23:2 (1968), 1–58 | DOI | MR | Zbl

[20] I. M. Gelfand, M. L. Tsetlin, “Konechnomernye predstavleniya gruppy unimodulyarnykh matrits”, Dokl. AN SSSR, 71:5 (1950), 825–828 | MR | Zbl

[21] R. Godement, “Theory of spherical functions. I”, Trans. Amer. Math. Soc., 73:3 (1952), 496–556 | DOI | MR | Zbl

[22] Harish-Chandra, “Representations of semi-simple Lie groups. II”, Trans. Amer. Math. Soc., 76 (1954), 26–65 | DOI | MR | Zbl

[23] S. M. Khoroshkin, “Irreducible representations of Lorentz groups”, Funct. Anal. Appl., 15:2 (1981), 114–122 | DOI | MR | Zbl | Zbl

[24] S. Khoroshkin, M. Nazarov, “Yangians and Mickelsson algebras. I”, Transform. Groups, 11:4 (2006), 625–658 ; arXiv: math/0606265 | DOI | MR | Zbl

[25] A. W. Knapp, Representation theory of semi-simple groups. An overview based on examples, Princeton Math. Ser., 36, Princeton University Press, Princeton, NJ, 1986 | MR | Zbl

[26] V. Lafforgue, $K$-théory bivariante pour les algèbres de Banach et conjecture de Baum–Connes, Thèse de doctorat, Université Paris-Sud, Paris, 1999

[27] R. P. Langlands, On classification of irreducible representations of real algebraic groups, Unpublished Manuscript, 1973

[28] J. Lepowsky, G. W. McCollum, “On determination of irreducible modules by restriction to a subalgebra”, Trans. Amer. Math. Soc., 176 (1973), 45–57 | DOI | MR | Zbl

[29] P.-O. Löwdin, “Angular momentum wavefunctions constructed by projector operators”, Rev. Modern Phys., 36 (1964), 966–976 | DOI | MR

[30] J. Mickelsson, “Step algebras of semi-simple subalgebras of Lie algebras”, Rep. Mathematical Phys., 4:4 (1973), 307–318 | DOI | MR | Zbl

[31] A. I. Molev, “A basis for representations of symplectic Lie algebras”, Comm. Math. Phys., 201:3 (1999), 591–618 | DOI | MR | Zbl

[32] A. I. Molev, “Yangians and transvector algebras”, Discrete Math., 246:1–3 (2002), 231–253 | DOI | MR | Zbl

[33] M. A. Naimark, Linear representations of the Lorentz group, The Macmillan, New York, 1964 | MR | MR | Zbl

[34] V. V. Shtepin, “Separation of multiple points of spectrum in the reduction $\mathrm{sp}(2n)\downarrow\mathrm{sp}(2n-2)$”, Functional Anal. Appl., 20:4 (1986), 336–338 | DOI | MR | Zbl

[35] P. Torasso, “Le théorème de Paley–Wiener pour l'espace des fonctions indéfinitement différentiables et à support compact sur un espace symétrique de type non-compact”, J. Funct. Anal., 26:2 (1977), 201–213 | DOI | MR | Zbl

[36] A. Young, “On quantitative substitutional analysis. VI”, Proc. London Math. Soc. (2), 31:2 (1931), 253–288 | DOI | Zbl

[37] D. P. Zhelobenko, “Opisanie nekotorogo klassa lineinykh predstavlenii gruppy Lorentsa”, Dokl. AN SSSR, 121:4 (1958), 585–589 | MR

[38] D. P. Zhelobenko, “Lineinye predstavleniya gruppy Lorentsa”, Dokl. AN SSSR, 126:5 (1959), 935–938 | MR | Zbl

[39] D. P. Zhelobenko, “The classical groups. Spectral analysis of their finite-dimensional representations”, Russ. Math. Surveys, 17:1 (1962), 1–94 | DOI | MR | Zbl

[40] D. P. Zhelobenko, “K teorii lineinykh predstavlenii kompleksnykh i veschestvennykh grupp Li”, Tr. MMO, 12, 1963, 53–98 | MR | Zbl

[41] D. P. Zhelobenko, “Garmonicheskii analiz na poluprostykh gruppakh Li. I”, Izv. AN SSSR. Ser. matem., 27:6 (1963), 1343–1394 | MR | Zbl

[42] D. P. Zhelobenko, “Symmetry in a class of elementary representations of a semisimple complex Lie group”, Funct. Anal. Appl., 1:2 (1967), 103–121 | DOI | MR | Zbl

[43] D. P. Želobenko, “The analysis of irreducibility in the class of elementary representations of a complex semisimple Lie group”, Math. USSR-Izv., 2:1 (1968), 105–128 | DOI | MR | Zbl

[44] D. P. Želobenko, “Operational calculus on a complex semisimple Lie group”, Math. USSR-Izv., 3:5 (1969), 881–916 | DOI | MR | Zbl

[45] D. P. Želobenko, “Harmonic analysis of functions on semisimple Lie groups. II”, Math. USSR-Izv., 3:6 (1969), 1183–1217 | DOI | MR | Zbl

[46] D. P. Zhelobenko, “On the irreducible representations of a complex semisimple Lie group”, Funct. Anal. Appl., 4:2 (1970), 163–165 | DOI | MR | Zbl

[47] D. P. Želobenko, Compact Lie groups and their representations, Transl. Math. Monogr., 40, Amer. Math. Soc., Providence, RI, 1973 | MR | MR | Zbl | Zbl

[48] D. P. Želobenko, “Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups”, Math. USSR-Izv., 5:3 (1971), 589–613 | DOI | MR | Zbl

[49] D. P. Želobenko, “Cyclic modules for a complex semisimple Lie group”, Math. USSR-Izv., 7:3 (1973), 597–510 | DOI | MR | Zbl

[50] D. P. Zhelobenko, Garmonicheskii analiz na poluprostykh kompleksnykh gruppakh Li, Sovrem. probl. matem., Nauka, M., 1974 | MR | Zbl

[51] D. P. Želobenko, “Discrete symmetry operators for reductive Lie groups”, Math. USSR-Izv., 10:5 (1976), 1003–1029 | DOI | MR | Zbl

[52] D. P. Zhelobenko, “On Gelfand–Zetlin bases for classical Lie algebras”, Representations of Lie groups and Lie algebras (Budapest, 1971), Akad. Kiadó, Budapest, 1985, 79–106 | MR | Zbl

[53] D. P. Zhelobenko, “An analogue of the Gel'fand–Tsetlin basis for symplectic Lie algebras”, Russian Math. Surveys, 42:6 (1987), 247–248 | DOI | MR | Zbl

[54] D. P. Zhelobenko, “An introduction to the theory of $S$-algebras over reductive Lie algebras”, Representations of Lie groups and related topics, Adv. Stud. Contemp. Math., 7, Gordon and Breach, New York, 1990, 155–221 | MR | Zbl

[55] D. P. Zhelobenko, Predstavleniya reduktivnykh algebr Li, Nauka, M., 1994 | MR | Zbl

[56] D. P. Zhelobenko, Osnovnye struktury i metody teorii predstavlenii, MTsNMO, M., 2004 | MR | Zbl

[57] D. P. Zhelobenko, Operatsionnoe ischislenie na kompleksnykh poluprostykh gruppakh Li, MTsNMO, M. (to appear)

[58] D. P. Zhelobenko, Gaussovy algebry, MTsNMO, M. (to appear)

[59] D. P. Želobenko, M. A. Naǐmark, “Description of completely irreducible representations of a semi-simple complex Lie group”, Soviet Math. Dokl., 7 (1966), 1403–1406 | MR | Zbl

[60] D. P. Želobenko, M. A. Naǐmark, “Description of the completely irreducible representations of a complex semisimple Lie group”, Math. USSR-Izv., 4:1 (1970), 59–83 | DOI | MR | Zbl