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This research demonstrates super duality between Whittaker module categories over Lie algebra and Lie superalgebra, indicating profound algebraic connections.
We establish a super duality as an equivalence between Whittaker module categories over a pair of classical Lie algebra and Lie superalgebra in the infinite-rank limit. Building on this result and utilizing the Losev–Shu–Xiao decomposition, we obtain a super duality which is an equivalence between module categories over a pair of finite W-algebras and W-superalgebras at the infinite-rank limit.
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Cheng et al. (2025) studied this question.
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