Orthogonal multiple flag varieties of finite type I: odd degree case. (English) Zbl 1383.22008
Summary: Let \(G\) be the split orthogonal group of degree \(2 n + 1\) over an arbitrary infinite field \(\mathbb{F}\) of \(\operatorname{char} \mathbb{F} \neq 2\). In this paper, we classify multiple flag varieties \(G / P_1 \times \cdots \times G / P_k\) of finite type. Here a multiple flag variety is said to be of finite type if it has a finite number of \(G\)-orbits with respect to the diagonal action of \(G\).
MSC:
| 22E46 | Semisimple Lie groups and their representations |
| 14L35 | Classical groups (algebro-geometric aspects) |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
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