有限W超代数与Clifford扭转的范畴等价性
Categorical Equivalences of Finite W-Superalgebras and Clifford Twists
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中文总结 AI 辅助
本文研究基础经典李超代数中有限W超代数的两种构造，证明其等价性并利用Skryabin等价分类其不可约表示。
中文摘要 AI 辅助
我们在基础经典李超代数𝔤中，与偶幂零元e相关，全面研究有限W超代数的两种构造方式，分别通过Whittaker模型和迷向子空间定义。我们证明两种表述均独立于构造中所作的各种选择，因此对于e的固定好的分次，最多产生两类W超代数的同构类。当存在两个非同构版本时，我们证明它们的差异恰好在于Clifford扩张。因此，当两个W超代数非同构时，它们的模范畴在Clifford扭转下等价。基于该等价性并利用Skryabin等价，我们通过𝔤上的广义Whittaker模对它们的不可约表示进行分类。
英文摘要
Associated with an even nilpotent element $e$ in a basic classical Lie superalgebra $\mathfrak{g}$, we study, in full generality, two constructions of finite $W$-superalgebras, defined via Whittaker models and isotropic subspaces, respectively. We prove that both formulations are independent of the various choices made in their constructions, thereby yielding, for a fixed good grading for $e$, at most two isomorphism classes of $W$-superalgebras. In the case when there are two non-isomorphic versions, we establish that they differ precisely by a Clifford extension. Consequently, when the two $W$-superalgebras are non-isomorphic, their module categories are equivalent up to a Clifford twist. Building on this equivalence and utilizing the Skryabin equivalence, we classify their irreducible representations in terms of generalized Whittaker modules over $\mathfrak{g}$
