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Multiple flag varieties of finite type. (English) Zbl 0951.14034
The authors give a complete classification of all dimension types of \(k\)-tuples \((P_1, \dots , P_k)\) of parabolic subgroups of \(Gl_n\), such that the diagonal action of \(Gl_n\) on \(G/P_1\times \cdots \times G/P_k\) has finitely many orbits. Also the orbits are classified in each case, and explicit representations are constructed.

14M15 Grassmannians, Schubert varieties, flag manifolds
20G15 Linear algebraic groups over arbitrary fields
14L30 Group actions on varieties or schemes (quotients)
14L35 Classical groups (algebro-geometric aspects)
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