Classifying relaxed highest-weight modules for admissible-level Bershadsky-Polyakov algebras

Autor:	Fehily, Zachary, Kawasetsu, Kazuya, Ridout, David
Rok vydání:	2020
Předmět:	Mathematics - Representation Theory High Energy Physics - Theory Mathematical Physics Mathematics - Quantum Algebra
Druh dokumentu:	Working Paper
DOI:	10.1007/s00220-021-04008-y
Popis:	The Bershadsky-Polyakov algebras are the minimal quantum hamiltonian reductions of the affine vertex algebras associated to $\mathfrak{sl}_3$ and their simple quotients have a long history of applications in conformal field theory and string theory. Their representation theories are therefore quite interesting. Here, we classify the simple relaxed highest-weight modules, with finite-dimensional weight spaces, for all admissible but nonintegral levels, significantly generalising the known highest-weight classifications [arxiv:1005.0185, arxiv:1910.13781]. In particular, we prove that the simple Bershadsky-Polyakov algebras with admissible nonintegral $\mathsf{k}$ are always rational in category $\mathscr{O}$, whilst they always admit nonsemisimple relaxed highest-weight modules unless $\mathsf{k}+\frac{3}{2} \in \mathbb{Z}_{\ge0}$. Comment: 35 pages, 7 figures, 1 table
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.03917 Zobrazit plný text záznamu View this record from Arxiv