2022/03/03 by Thomas Creutzig, Andrew R. Linshaw, Creutzig, Thomas +5
Mathematics · Medicine · #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Ophthalmology and Eye Disorders #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2203.01843
openalex publication_date 2022/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Feigin-Frenkel duality is the isomorphism between the principal W-algebras of a simple Lie algebra \mathfrakg and its Langlands dual Lie algebra L\mathfrakg. 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-algebras are isomorphic. A natural question is whether the duality between affine cosets can be enhanced to a duality between the full W-algebras. 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.