We provide a weaker version of the generalized lifting property which holds in complete generality for all finite Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also describe some combinatorial properties of the associated polytopes.

中文翻译：

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弱广义提升性、Bruhat 区间和 Coxeter 拟阵

我们提供了广义提升性质的较弱版本，它对所有有限 Coxeter 群完全通用，我们用它来证明有限 Coxeter 群的每个抛物线 Bruhat 区间都是 Coxeter 拟阵。我们还描述了相关多胞体的一些组合特性。