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arXiv · 2007.00396

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

Drazen Adamovic·Kazuya Kawasetsu·David Ridout
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Abstract

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.

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Drazen Adamovic, Kazuya Kawasetsu, David Ridout. 2020-07-01. A realisation of the Bershadsky--Polyakov algebras and their relaxed modules. https://doi.org/10.1007/s11005-021-01378-1

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