Super duality for Whittaker modules and finite W-algebras

2024/10/11 by Shun‐Jen Cheng, Weiqiang Wang, Cheng, Shun-Jen +1
Mathematics · #17B10 #17B20 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Mathematical Analysis and Transform Methods #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2410.08617

openalex publication_date 2024/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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