We study tilting and projective‐injective modules in a parabolic BGG category $\mathcal{O}$ for an arbitrary classical Lie superalgebra. We establish a version of Ringel duality for this type of Lie superalgebras which allows to express the characters of tilting modules in terms of those of simple modules in that category. We also obtain a classification of projective‐injective modules in the full BGG category $\mathcal{O}$ for all simple classical Lie superalgebras. We then classify and give an explicit combinatorial description of parabolic subalgebras of the periplectic Lie superalgebras and apply our results to study their tilting modules in more detail.

中文翻译：

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经典李超代数的倾斜模块

我们研究抛物线BGG类别中的倾斜和射影-射流模块 $\mathcal{Ø}$一个任意的经典李超代数。我们为这种李超代数建立了林格对偶的一个版本，该版本允许以该类别中的简单模块的形式来表达倾斜模块的特征。我们还获得了完整BGG类别中的射影-内射模块的分类$\mathcal{Ø}$适用于所有简单的经典李超代数。然后，我们对立面李超代数的抛物线子代数进行分类并给出明确的组合描述，并将我们的结果应用于更详细地研究其倾斜模块。