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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.

MSC:
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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