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A realisation of the Bershadsky--Polyakov algebras and their relaxed modules (2007.00396v2)
Published 1 Jul 2020 in math.QA, hep-th, math-ph, math.MP, and math.RT
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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