Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series
Funkcionalʹnyj analiz i ego priloženiâ, Tome 15 (1981) no. 4, pp. 53-66.

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G. I. Olshanskii. Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series. Funkcionalʹnyj analiz i ego priloženiâ, Tome 15 (1981) no. 4, pp. 53-66. http://geodesic.mathdoc.fr/item/FAA_1981_15_4_a4/

[1] Olshanskii G.I., “Unitarnye predstavleniya beskonechnomernykh klassicheskikh grupp $U(p,\infty)$, $SO_0(p,\infty)$, $S_p(p,\infty)$ i sootvetstvuyuschikh grupp dvizhenii”, Funkts. analiz, 12:3 (1978), 32–44 | MR

[2] Olshanskii G.I., “Konstruktsiya unitarnykh predstavlenii beskonechnomernykh klassicheskikh grupp”, DAN SSSR, 250:2 (1980), 284–288 | MR

[3] Vinberg E.B., “Invariantnye vypuklye konusy i uporyadocheniya v gruppakh Li”, Funkts. analiz, 14:1 (1980), 1–13 | MR | Zbl

[4] Paneitz S.M., Causal structures in Lie groups and applications to stability of differential equations, Ph. D., MIT, May, 1980 | MR

[5] Graev M.I., “Unitarnye predstavleniya veschestvennykh prostykh grupp Li”, Trudy Mosk. matem. ob-va, 7, 1958, 335–389 | MR | Zbl

[6] Brunet M., Kramer P., “Complex extension of the representation of the symplectic group associated with canonical commutation relations”, Lecture Notes in Physics, 50, 1967, 441–449 | DOI | MR

[7] Nagano T., “Transformation groups on compact symmetric spaces”, Trans. Amer. Math. Soc., 118, 1965, 428–453 | DOI | MR | Zbl

[8] Gelfand I.M., Gindikin S.G., “Kompleksnye mnogoobraziya, ostovy kotorykh – poluprostye veschestvennye gruppy, i analiticheskie diskretnye serii predstavlenii”, Funkts. analiz, 11:4 (1977), 19–27 | MR

[9] Streater R.F., “Representations of the oscillator group”, Comm. Math. Phys., 4 (1967), 217–236 | DOI | MR | Zbl

[10] Segal I.E., Mathematical cosmology and extragalactical astronomy, Acad. Press, N. Y., 1976 | MR

[11] Kashiwara M., Vergne M., “On the Segal–Shale–Weil representations and harmonic polynomials”, Invent. Math., 44:1 (1978), 1–47 | DOI | MR | Zbl

[12] Olshanskii G.I., “Opisanie unitarnykh predstavlenii so starshim vesom dlya grupp i $U(p,q)\tilde{\hphantom{h}}$”, Funkts. analiz, 14:3 (1980), 32–44 | MR

[13] Scull S.C., “Positive operators and automorphic groups of bounded symmetric domains”, Reports Math. Phys., 10:1 (1976), 1–7 | DOI | MR | Zbl

[14] Harish-Chandra, “Representations of semisimple Lie groups. IV–VI”, Amer. J. Math., 77 (1955), 743–777 ; 78 (1956), 1–41 ; 78 (1956), 564–628 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[15] Leng S., $SL_2(R)$, Mir, M., 1977

[16] Nelson E., “Analytic vectors”, Ann. Math., 70 (1959), 572–615 | DOI | MR | Zbl

[17] Lüscher M., Mack G., “Global conformal invariance in quantum field theory”, Comm. Math. Phys., 41:3 (1975), 203–234 | DOI | MR

[18] Takeuchi M., “Cell decompositions and Morse equalities on certain symmetric spaces”, J. Fac. Sci. Univ. Tokyo, 12 (1965), 81–192 | DOI | MR

[19] Khelgason S., Differentsialnaya geometriya i simmetricheskie prostranstva, Mir, M., 1964

[20] Drucker D., Exceptional Lie algebras and the structm-e of Hermitian symmetric spaces, Mem. Amer. Math. Soc., 208, 1978 | MR | Zbl

[21] Oshima T., Matsuki T., “Orbits on affine symmetric spaces under the action of the isotropy subgroups”, J. Math. Soc. Japan, 32:2 (1980), 399–414 | DOI | MR | Zbl

[22] Carmona J., “Les sous-algebres de Cartan réelles et la frontière d'une orbite ouverte dans une varieté de drapeaux”, Manuscr. Math., 10:1 (1973), 1–33 | DOI | MR | Zbl

[23] Teoriya algebr Li. Topologiya grupp Li, Seminar «Sofus Li», IL, M., 1962