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A class of parabolic $$k$$-subgroups associated with symmetric $$k$$-varieties. (English) Zbl 0912.20041
Let $$G$$ be a connected reductive algebraic group defined over a field $$k$$ of characteristic not 2, $$\sigma$$ an involution of $$G$$ defined over $$k$$, $$H$$ a $$k$$-open subgroup of the fixed point group of $$\sigma$$, $$H_k$$ the set of $$k$$-rational points of $$H$$. The authors give a description of the $$H_k$$-conjugacy classes of the $$\sigma$$-split parabolic $$k$$-subgroups of $$G$$ for general symmetric $$k$$-varieties. In a number of cases, this description can be refined to give a more detailed description.
Reviewer: V.L.Popov (Moskva)

##### MSC:
 20G15 Linear algebraic groups over arbitrary fields 14M17 Homogeneous spaces and generalizations 22E15 General properties and structure of real Lie groups 22E46 Semisimple Lie groups and their representations 53C35 Differential geometry of symmetric spaces 20G20 Linear algebraic groups over the reals, the complexes, the quaternions
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