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2020年7月8日

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

  • Zachary Fehily
  • ,
  • Kazuya Kawasetsu
  • ,
  • David Ridout

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 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 $\mathsf{k}+\frac{3}{2} \in \mathbb{Z}_{\ge0}$.

リンク情報
arXiv
http://arxiv.org/abs/arXiv:2007.03917
Arxiv Url
http://arxiv.org/abs/2007.03917v1
Arxiv Url
http://arxiv.org/pdf/2007.03917v1 本文へのリンクあり

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