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Some results on algebraic groups with involutions. (English) Zbl 0628.20036

Algebraic groups and related topics, Proc. Symp., Kyoto and Nagoya/Jap. 1983, Adv. Stud. Pure Math. 6, 525-543 (1985).
[For the entire collection see Zbl 0561.00006.]
Let G be a reductive linear algebraic group over an algebraically closed field of characteristic not 2, and let \(\theta\) be an involution of G. Denote by K the fixed point group of \(\theta\) and by B a Borel subgroup. Then K has finitely many orbits in the flag manifold G/B. The author establishes some basic facts about these orbits. He gives a rather explicit description of these orbits as algebraic varieties, studies K- fixed vectors in G-modules, and describes orbit closures.

MSC:

20G05 Representation theory for linear algebraic groups
14M15 Grassmannians, Schubert varieties, flag manifolds
20G15 Linear algebraic groups over arbitrary fields

Citations:

Zbl 0561.00006