In this paper the authors introduce a class of parabolic subalgebras for classical simple Lie superalgebras associated to the detecting subalgebras introduced by Boe, Kujawa and Nakano. These parabolic subalgebras are shown to have good cohomological properties governed by the Bott-Borel-Weil theorem involving the zero component of the Lie superalgebra in conjunction with the odd roots. These results are later used to verify an open conjecture given by Boe, Kujawa and Nakano pertaining to the equality of various support varieties.

中文翻译：

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关于简单经典李超代数的BBW抛物线

在本文中，作者介绍了与Boe，Kujawa和Nakano引入的检测子代数相关的经典简单Lie超级代数的一类抛物子代数。这些抛物子代数具有良好的同调性，受Bott-Borel-Weil定理支配，该定理涉及Lie超代数的零分量以及奇数根。这些结果随后被用于验证Boe，Kujawa和Nakano提出的关于各种支持品种平等的公开猜想。