This paper explores the possible use of Schubert cells and Schubert varieties in finite geometry, particularly in regard to the question of whether these objects might be a source of understanding of ovoids or provide new examples. The main result provides a characterization of those Schubert cells for finite Chevalley groups which have the first property (thinness) of ovoids. More importantly, perhaps this short paper can help to bridge the modern language barrier between finite geometry and representation theory. For this purpose, this paper includes very brief surveys of the powerful lattice theory point of view from finite geometry and the powerful method of indexing points of flag varieties by Chevalley generators from representation theory.

中文翻译：

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舒伯特细胞的厚度作为发病结构

本文探讨了舒伯特细胞和舒伯特变体在有限几何中的可能用途，特别是关于这些物体是否可能成为理解卵形体的来源或提供新例子的问题。主要结果提供了有限 Chevalley 群的舒伯特单元的表征，这些群具有第一个属性 (薄度) 的卵形。更重要的是，也许这篇简短的论文可以帮助弥合有限几何和表示论之间的现代语言障碍。为此，本文对有限几何中强大的格理论观点和表示论中 Chevalley 生成器索引标志品种点的强大方法进行了非常简短的调查。