Modularity of BershadskyPolyakov minimal models
Abstract
The BershadskyPolyakov algebras are the original examples of nonregular Walgebras, obtained from the affine vertex operator algebras associated with $\mathfrak{sl}_3$ by quantum hamiltonian reduction. In [arXiv:2007.03917], we explored the representation theories of the simple quotients of these algebras when the level $\mathsf{k}$ is nondegenerateadmissible. Here, we combine these explorations with Adamović's inverse quantum hamiltonian reduction functors to study the modular properties of BershadskyPolyakov characters and deduce the associated Grothendieck fusion rules. The results are not dissimilar to those already known for the affine vertex operator algebras associated with $\mathfrak{sl}_2$, except that the role of the Virasoro minimal models in the latter is here played by the minimal models of Zamolodchikov's $\mathsf{W}_3$ algebras.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10336
 Bibcode:
 2021arXiv211010336F
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Representation Theory
 EPrint:
 37 pages, 1 figure