Geodesic
Open symmetric orbits of reductive groups in symmetric $R$-spaces
Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 406-418 
B. O. Makarevich. Open symmetric orbits of reductive groups in symmetric $R$-spaces. Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 406-418. http://geodesic.mathdoc.fr/item/SM_1973_20_3_a5/
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     title = {Open symmetric orbits of reductive groups in symmetric $R$-spaces},
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Voir la notice de l'article provenant de la source Math-Net.Ru

One considers symmetric spaces which are simultaneously $R$-spaces, i.e. factor spaces of semisimple Lie groups by parabolic subgroups. By a symmetric domain is meant a domain, each point of which is an isolated fixed point of an involutive transformation of the domain. In the work one finds an explicit list of all reductive groups in symmetric $R$-spaces which have open symmetric orbits. For spaces which are connected by means of the Kantor–Koecher construction with semisimple Jordan algebras, the problem is solved by means of the reduction obtained by A. A. Rivilis and some general propositions supplementing his results. Moreover, one applies other methods based on the theory of representations and using the theorem on decompositions of semisimple Lie groups. Bibliography: 10 titles.

[1] M. Berger, “Espaces symétriques non compacts”, Ann. scient. Ecole norm. supér, 74 (1957), 85–177 | MR

[2] E. B. Vinberg, “Odnorodnye vypuklye konusy”, Trudy Mosk. matem. ob-va, XII (1963), 303–358 | MR

[3] I. L. Kantor, “Obschaya norma iordanovoi algebry i geometriya nekotorykh grupp preobrazovanii”, Trudy seminara po vekt. i tenz. analizu, 14 (1968), 114–143 | MR | Zbl

[4] I. L. Kantor, A. I. Sirota, A. S. Solodovnikov, “Odin klass rimanovykh prostranstv s rasshiryaemoi gruppoi dvizhenii i obobschenie modeli Puankare”, DAN SSSR, 173:2 (1967), 511–514 | MR | Zbl

[5] M. Koecher, “Imbedding of Jordan algebras into Lie algebras”, Amer. J. Math., 89:3 (1967), 787–816 | DOI | MR | Zbl

[6] O. Loos, Symmetric spaces, v. I, Benjamin, New York, 1969 | Zbl

[7] A. A. Rivilis, “Odnorodnye lokalno simmetricheskie oblasti v odnorodnykh prostranstvakh, assotsiirovannykh s poluprostymi iordanovymi algebrami”, Matem. sb., 82 (124) (1970), 409–422 | MR | Zbl

[8] A. A. Rivilis, “Odnorodnye lokalno simmetricheskie oblasti v konformnykh prostranstvakh”, DAN SSSR, 184:3 (1969), 558–561 | MR | Zbl

[9] G. Freidental, “Oktavy, osobye gruppy i oktavnaya geometriya”, Matematika, 1:1 (1957), 117–153

[10] A. L. Onischik, “Razlozheniya reduktivnykh grupp Li”, Matem. sb., 80 (122) (1969), 553–599 | Zbl