×

Homogeneous domains on flag manifolds and spherical subgroups of semisimple Lie groups. (English. Russian original) Zbl 0439.53055

Funct. Anal. Appl. 12, 168-174 (1979); translation from Funkts. Anal. Prilozh. 12, No. 3, 12-19 (1978).

MSC:

53C30 Differential geometry of homogeneous manifolds
22E46 Semisimple Lie groups and their representations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] É. B. Vinberg, ”Theory of homogeneous convex cones,” Tr. Mosk. Mat. Ob-va,12, 303–358 (1963). · Zbl 0138.43301
[2] É. B. Vinberg, ”Construction of the automorphism group of a homogeneous convex cone,” Tr. Mosk. Mat. Ob-va,13, 56–83 (1965). · Zbl 0224.17010
[3] É. B. Vinberg, S. G. Gindikin, and I. I. Pyatetskii-Shapiro, ”On the classification and canonical realization of complex homogeneous bounded domains,” Tr. Mosk. Mat. Ob-va,12, 359–388 (1963).
[4] A. L. Onishchik, ”Decomposition of reductive Lie groups,” Mat. Sb.,80, 553–559 (1969). · Zbl 0222.22011
[5] A. L. Onishchik, ”On extensions of transitive transformation groups,” Izv. Vyssh. Uchebn. Zaved., Mat.,3, 52–64 (1977).
[6] J. A. Wolf, ”The action of a real semisimple group on a complex flag manifold. I. Orbit structure and holomorphic arc components,” Bull. Am. Math. Soc.,75, No. 6, 1121–1237 (1969). · Zbl 0183.50901 · doi:10.1090/S0002-9904-1969-12359-1
[7] A. A. Rivilis, ”Homogeneous locally symmetric domains in conformal space,” Dokl. Akad. Nauk SSSR,184, No. 3, 558–561 (1969). · Zbl 0188.25802
[8] A. A. Rivilis, ”Homogeneous locally symmetric domains in homogeneous spaces associated with semisimple Jordan algebras,” Mat. Sb., 409–422 (1970). · Zbl 0205.26005
[9] B. O. Makarevich, ”Open symmetric orbits of reductive groups in symmetric R-spaces,” Mat. Sb.,91, 390–401 (1973). · Zbl 0279.53047
[10] B. N. Kimel’fel’d, ”Homogeneous domains on a conformal sphere,” Mat. Zametki,8, No. 3, 321–328 (1970).
[11] F. M. Malyshev, ”Local decomposition of pseudoorthogonal groups,” Mat. Zametki,16, No. 4, 633–643 (1974).
[12] B. N. Kimel’fel’d, ”Homogeneous domains on flag manifolds of rank 1,” Dokl. Akad. Nauk SSSR,229, No. 1, 23–26 (1976).
[13] B. N. Kimel’fel’d, ”Open orbits of reductive groups on complex quadrics,” Soobshch. Akad. Nauk Gruz. SSR,81, No. 2, 305–308 (1976).
[14] F. J. Servedio, ”Prehomogeneous vector spaces and varieties,” Trans. Am. Math. Soc.,176, 421–444 (1973). · Zbl 0266.20043 · doi:10.1090/S0002-9947-1973-0320173-7
[15] T. Vust, ”Opération de groupes réductifs dans un type de cônes presques homogènes,” Bull. Soc. Math. France,102, No. 3, 317–333 (1974). · Zbl 0332.22018
[16] A. Borel and Harish-Chandra, ”Arithmetic subgroups of algebraic groups,” Matematika,8, No. 2, 19–71 (1964). · Zbl 0119.37001
[17] C. Chevalley, Theory of Lie Groups, Academic Press (1957). · Zbl 0063.00842
[18] E. Cartan, ”Sur la détermination d’un système orthogonal complet dans un espace de Riemann symetrique clos,” Rend. Circolo Mat. Palermo,53, 217–252 (1929) (Oevres complètes, Part 1, Vol. 2 (1952), pp. 1045–1080). · JFM 55.1029.01 · doi:10.1007/BF03024106
[19] I. M. Gel’fand, ”Spherical functions on symmetric Riemannian spaces,” Dokl. Akad. Nauk SSSR,70, No. 1, 5–8 (1950).
[20] R. Godement, ”A theory of spherical functions. I,” Trans. Am. Math. Soc.,73, No. 3, 496–556 (1952). · Zbl 0049.20103 · doi:10.1090/S0002-9947-1952-0052444-2
[21] M. Krämer, ”Multiplicity free subgroups of compact connected Lie groups,” Archiv Math.,27, No. 1, 28–36 (1976). · Zbl 0322.22011 · doi:10.1007/BF01224637
[22] A. A. Kirillov, Elements of the Theory of Representations [in Russian], Nauka, Moscow (1972). · Zbl 0249.22012
[23] M. Rosenlicht, ”Some basic theorems on algebraic groups,” Am. J. Math.,78, No. 2, 401–443 (1956). · Zbl 0073.37601 · doi:10.2307/2372523
[24] V. L. Popov, ”Picard groups of homogeneous spaces of linear algebraic groups and homogeneous vector bundles,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, 294–322 (1974). · Zbl 0298.14023
[25] I. R. Shatarevich, Basic Algebraic Geometry, Springer-Verlag (1974).
[26] M. Rosenlicht, ”Some rationality questions on algebraic groups,” Ann. Mat. Pura Appl.,43, 25–50 (1957). · Zbl 0079.25703 · doi:10.1007/BF02411903
[27] É. B. Vinberg and A. L. Onishchik, Seminar on Algebraic Groups and Lie Groups 1967/1968 [in Russian], Moscow State Univ. (1969). · Zbl 0876.22001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.