Duality via convolution of W-algebras

Creutzig T, Linshaw AR, Nakatsuka S, Sato R (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Selecta Mathematica-New Series Springer Verlag (Germany)

Book Volume: 31

Article Number: 56

Journal Issue: 3

DOI: 10.1007/s00029-025-01050-9

Abstract

Feigin-Frenkel duality is the isomorphism between the principal W-algebras of a simple Lie algebra g and its Langlands dual Lie algebra Lg. A generalization of this duality to a larger family of W-algebras called hook-type was recently conjectured by Gaiotto and Rapčák and proved by the first two authors. It says that the affine cosets of two different hook-type W-(super)algebras are isomorphic. A natural question is whether the duality between the affine cosets can be enhanced to reconstruct one W-algebra from the other. There is a convolution operation that maps a hook-type W-algebra W to a certain relative semi-infinite cohomology of W tensored with a suitable kernel VOA. The first two authors conjectured previously that this cohomology is isomorphic to the Feigin-Frenkel dual hook-type W-algebra. Our main result is a proof of this conjecture.

Authors with CRIS profile

Thomas Creutzig Lehrstuhl für Darstellungstheorie Shigenori Nakatsuka Lehrstuhl für Darstellungstheorie

Involved external institutions

University of Denver US United States (USA) (US) Aichi Institute of Technology (AIT) / 愛知工業大学 JP Japan (JP)

How to cite

APA:

Creutzig, T., Linshaw, A.R., Nakatsuka, S., & Sato, R. (2025). Duality via convolution of W-algebras. Selecta Mathematica-New Series, 31(3). https://doi.org/10.1007/s00029-025-01050-9

MLA:

Creutzig, Thomas, et al. "Duality via convolution of W-algebras." Selecta Mathematica-New Series 31.3 (2025).

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