Orthogonal multiple flag varieties of finite type I : Odd degree case

Abstract

Let $G$ be the split orthogonal group of degree $2n+1$ over an arbitrary field $\mathbb{F}$ of $\mathrm{char}\mathbb{F}\ne 2$. 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 called of finite type if it has a finite number of $G$-orbits with respect to the diagonal action of $G$ when $|\mathbb{F}|=\infty$.

60 pages. There was a mistake on ${\mathbb{F}}^{\times }/(\mathbb{F}\times {)}^2$ in the first version. The main theorem is reformed