Ol’shanskij, G. I. Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series. (English) Zbl 0503.22011 Funct. Anal. Appl. 15, 275-285 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 46 Documents MSC: 22E60 Lie algebras of Lie groups 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties 22A25 Representations of general topological groups and semigroups 22D12 Other representations of locally compact groups Keywords:Lie semigroups with involution; contractions in a Hilbert space; finite- dimensional classical groups; invariant convex cones; holomorphic representations Citations:Zbl 0484.22023 PDF BibTeX XML Cite \textit{G. I. Ol'shanskij}, Funct. Anal. Appl. 15, 275--285 (1982; Zbl 0503.22011) Full Text: DOI OpenURL References: [1] G. I. Ol’shanskii, ”Unitary representations of the infinite-dimensional classical groups U(p, ?), SO 0(p, ?), Sp(p, ?) and of the corresponding motion groups,” Funkts. Anal. Prilozhen.,12, No. 3, 32-44 (1978). · Zbl 0392.22012 [2] G. I. Ol’shanskii, ”Construction of unitary representations of infinite-dimensional classical groups,” Dokl. Akad. Nauk SSSR,250, No. 2, 284-288 (1980). [3] É. B. Vinberg, ”Invariant cones and orderings in Lie groups,” Funkts. Anal. Prilozhen.,14, No. 1, 1-13 (1980). · Zbl 0452.22014 [4] S. M. Paneitz, ”Causal structures in Lie groups and applications to stability of ordinary differential equations,” Ph. D. Thesis, MIT, May, 1980. [5] M. I. Graev, ”Unitary representations of real simple Lie groups,” Tr. Moskov. Mat. Ob-va.,7, 335-389 (1958) [Amer. Math. Soc. Translations, Ser. 2,66, 1-62 (1968)]. [6] M. Brunet and P. Kramer, ”Complex extension of the representation of the symplectic group associated with canonical commutation relations,” Lect. Notes Phys.,50, 441-449 (1967). [7] T. Nagano, ”Transformations groups on compact symmetric spaces,” Trans. Am. Math. Soc.,118, 428-453 (1965). · Zbl 0151.28801 [8] I. M. Gel’fand and S. G. Gindikin, ”Complex manifolds whose skeletons are semisimple real Lie groups, and analytic discrete series of representations,” Funkts. Anal. Prilozhen.,11, No. 4, 19-27 (1977). [9] R. F. Streater, ”Representations of the oscillator group,” Commun. Math. Phys.,4, 217-236 (1967). · Zbl 0155.32503 [10] I. E. Segal, Mathematical Cosmology and Extragalactic Astronomy, Academic Press, New York (1976). [11] M. Kashiwara and M. Vergne, ”On the Segal?Shale?Weil representations and harmonic polynomials,” Invent. Math.,44, No. 1, 1-47 (1978). · Zbl 0375.22009 [12] G. I. Ol’shanskii, ”Description of unitary representations with highest weight for groups U(p, q)\(\sim\),” Funkts. Anal. Prilozhen.,14, No. 3, 32-44 (1980). · Zbl 0439.22019 [13] S. C. Scull, ”Positive operators and automorphic groups of bounded symmetric domains,” Reports Math. Phys.,10, No. 1, 1-7 (1976). · Zbl 0357.47023 [14] Harish-Chandra, ”Representations of semisimple Lie groups,” IV?VI, Am.J.Math.,77, 743-777 (1955);78, 1-41 (1956);78, 564-628 (1956). · Zbl 0066.35603 [15] S. Lang, SL2(R), Addison-Wesley, Reading, Mass. (1975). [16] E. Nelson, ”Analytic vectors,” Ann. Math.,70, 572-615 (1959). · Zbl 0091.10704 [17] M. Lüscher and G. Mack, ”Global conformal invariance in quantum field theory,” Commun. Math. Phys.,41, No. 3, 203-234 (1975). [18] M. Takeuchi, ”Cell decompositions and Morse equalities on certain symmetric spaces,” J. Fac. Sci. Univ. Tokyo,12, 81-192 (1965). · Zbl 0144.22804 [19] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York (1962). · Zbl 0111.18101 [20] D. Drucker, ”Exceptional Lie algebras and the structure of Hermitian symmetric spaces,” Mem. Am. Math. Soc.,208 (1978). · Zbl 0395.17009 [21] T. Oshima and T. Matsuki, ”Orbits of affine symmetric spaces under the action of the isotropy sub-groups,” J. Math. Soc. Jpn.,32, No. 2, 399-414 (1980). · Zbl 0451.53039 [22] J. Carmona, ”Les sous-algebres de Cartan réelles et la frontière d’une orbite ouverte dans une varieté des drapeaux,” Manuscr. Math.,10, No. 1, 1-33 (1973). · Zbl 0274.22019 [23] Theory of Lie Algebras. Topology of Lie Groups (Seminar ”S. Lie”) [Russian translation], IL, Moscow (1962). 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.