no. 4
Super duality for Whittaker modules and finite $W$-algebras
Cheng, Shun-Jen1; Wang, Weiqiang2
1 Institute of Mathematics, Academia Sinica, Taipei, Taiwan 10617
2 Department of Mathematics, University of Virginia, Charlottesville, VA 22903, USA
Annals of Representation Theory, Volume 2 (2025) no. 4, pp. 505-535.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/art.28
Classification: 17B10, 17B20
Keywords: Whittaker modules, lie superalgebras, finite $W$-algebras

Cheng, Shun-Jen 1; Wang, Weiqiang 2

1 Institute of Mathematics, Academia Sinica, Taipei, Taiwan 10617
2 Department of Mathematics, University of Virginia, Charlottesville, VA 22903, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Cheng, Shun-Jen; Wang, Weiqiang. Super duality for Whittaker modules and finite $W$-algebras. Annals of Representation Theory, Volume 2 (2025) no. 4, pp. 505-535. doi : 10.5802/art.28. https://art.centre-mersenne.org/articles/10.5802/art.28/

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