Journal article

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

Drazen Adamovic, Kazuya Kawasetsu, David Ridout

LETTERS IN MATHEMATICAL PHYSICS | SPRINGER | Published : 2021

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 sl2 and osp(1 | 2) given in Adamović (Commun Math Phys 366:1025–1067, 2019). Relaxed highest-weight modules are likewise constructed, conditions for their irreducibility are established, and their characters are explicitly computed, generalising the character formulae of Kawasetsu and Ridout (Commun Math Phys 368:627–663, 2019).

University of Melbourne Researchers

Grants

Awarded by European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme


Awarded by JSPS Kakenhi Grant


Awarded by Australian Research Council


Awarded by Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers


Funding Acknowledgements

We thank Thomas Creutzig and Zac Fehily for discussions relating to the results presented here. D.A. is partially supported by the QuantiXLie Centre of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme (KK.01.1.1.01.0004). KK's research is partially supported by MEXT Japan "Leading Initiative for Excellent Young Researchers (LEADER)", JSPS Kakenhi Grant numbers 19KK0065 and 19J01093 and Australian Research Council Discovery Project DP160101520. DR's research is supported by the Australian Research Council Discovery Project DP160101520 and the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers CE140100049.