Weight module classifications for Bershadsky–Polyakov algebras
Abstrak
The Bershadsky-Polyakov algebras are the subregular quantum Hamiltonian reductions of the affine vertex operator algebras associated associated with [Formula: see text]. In (D. Adamović, K. Kawasetsu and D. Ridout, A realisation of the Bershadsky–Polyakov algebras and their relaxed modules, Lett. Math. Phys. 111 (2021) 38, arXiv:2007.00396 [math.QA]), we realized 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 has the property that the result is 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 (Z. Fehily, K. Kawasetsu and D. Ridout, Classifying relaxed highest-weight modules for admissible-level Bershadsky–Polyakov algebras, Comm. Math. Phys. 385 (2021) 859–904, 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=-[Formula: see text], which is new.
Topik & Kata Kunci
Penulis (3)
Dražen Adamović
Kazuya Kawasetsu
David Ridout
Akses Cepat
- Tahun Terbit
- 2023
- Bahasa
- en
- Total Sitasi
- 9×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1142/s0219199723500633
- Akses
- Open Access ✓