2023/06/26 by Fehily, Zachary · 2 citations
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2306.14673
Originating in the work of A.M. Semikhatov and D. Adamović, inverse reductions are embeddings involving W-algebras corresponding to the same Lie algebra but different nilpotent orbits. Here, we show that an inverse reduction embedding between the affine \mathfraksln+1 vertex operator algebra and the minimal \mathfraksln+1 W-algebra exists. This generalises the realisations for n=1,2 in [arXiv:1711.11342, arXiv:2110.15203]. A similar argument is then used to show that inverse reduction embeddings exists between all hook-type \mathfraksln+1 W-algebras, which includes the principal/regular, subregular, minimal \mathfraksln+1 W-algebras, and the affine \mathfraksln+1 vertex operator algebra. This generalises the regular-to-subregular inverse reduction of [arXiv:2111.05536], and similarly uses free-field realisations and their associated screening operators.