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September 17, 2025Annals of representation theory1 citationsOpen Access

Super duality for Whittaker modules and finite W-algebras

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SCShun‐Jen ChengNational Yang Ming Chiao Tung UniversityWWWeiqiang WangNortheast Petroleum University

Key Points

  • The study establishes a super duality, providing an equivalence between Whittaker module categories for classical Lie algebras.
  • Key findings showcase equivalences between module categories of finite W-algebras and W-superalgebras in high-rank limits.
  • Using the Losev–Shu–Xiao decomposition streamlines the understanding of these dualities and their implications for module categories.
  • The findings highlight significant algebraic structures that underpin the relationships between superalgebras and their classical counterparts.

Abstract

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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Cite This Study

Cheng et al. (2025) studied this question.

synapsesocial.com/papers/68d45b2931b076d99fa5db4dhttps://doi.org/10.5802/art.28
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