2020年7月1日

# A realisation of the Bershadsky--Polyakov algebras and their relaxed modules

• ,
• Kazuya Kawasetsu
• ,
• David Ridout

We present a realisation of the universal/simple Bershadsky--Polyakov vertex
algebras as subalgebras of the tensor product of the universal/simple
Zamolodchikov vertex algebras and an isotropic lattice vertex algebra. This
generalises the realisation of the universal/simple affine vertex algebras
associated to $\mathfrak{sl}_2$ and $\mathfrak{osp}(1|2)$ given in
arXiv:1711.11342. Relaxed highest-weight modules are likewise constructed,
conditions for their irreducibility are established, and their characters are
explicitly computed, generalising the character formulae of arXiv:1803.01989.

リンク情報
arXiv
http://arxiv.org/abs/arXiv:2007.00396
Arxiv Url
http://arxiv.org/abs/2007.00396v1
Arxiv Url
http://arxiv.org/pdf/2007.00396v1 本文へのリンクあり

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