This article is cited in 11 papers

Open symmetric orbits of reductive groups in symmetric $R$-spaces

B. O. Makarevich


Abstract: 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.

UDC: 519.46

MSC: Primary 22E05, 57E20; Secondary 17C20

Received: 25.10.1972

 English version: Mathematics of the USSR-Sbornik, 1973, 20:3, 406–418

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