2023/03/07 by Adamovic, Drazen, Kawasetsu, Kazuya, Ridout, David · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2303.03713
The Bershadsky--Polyakov algebras are the subregular quantum hamiltonian reductions of the affine vertex operator algebras associated with \mathfraksl3. In arXiv:2007.00396 [math.QA], we realised these algebras in terms of the regular reduction, Zamolodchikov's W3-algebra, and an isotropic lattice vertex operator algebra. We also proved that a natural construction of relaxed highest-weight Bershadsky--Polyakov modules gives modules that are generically irreducible. Here, we prove that this construction, when combined with spectral flow twists, gives a complete set of irreducible weight modules whose weight spaces are finite-dimensional. This gives a simple independent proof of the main classification theorem of arXiv:2007.03917 [math.RT] for nondegenerate admissible levels and extends this classification to a category of weight modules. We also deduce the classification for the nonadmissible level k=-(7)/(3), which is new.