Journal article
Weight module classifications for Bershadsky-Polyakov algebras
D Adamović, K Kawasetsu, D Ridout
Communications in Contemporary Mathematics | WORLD SCIENTIFIC PUBL CO PTE LTD | Published : 2024
Abstract
The Bershadsky-Polyakov algebras are the subregular quantum Hamiltonian reductions of the affine vertex operator algebras associated associated with 3. In (D. Adamović, K. Kawasetsu and D. Ridout, A realisation of the Bershadsky-Polyakov algebras and their relaxed modules, Lett. Math. Phys. 111 (2021) 38, arXiv:2007.00396 [math.QA]), we realized these algebras in terms of the regular reduction, Zamolodchikov's W3-algebra, and an isotropic lattice vertex operator algebra. We also proved that a natural construction of relaxed highest-weight Bershadsky-Polyakov modules has the property that the result is generically irreducible. Here, we prove that this construction, when combined with spectral..
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Grants
Awarded by Japan Society for the Promotion of Science
Funding Acknowledgements
We thank Thomas Creutzig, Justine Fasquel, Zac Fehily, Slava Futorny, Chris Ray-mond and Simon Wood for discussions related to the material presented here.D. A. is partially supported by the Croatian Science Foundation under the project IP-2022-10-9006 and by the project "Implementation of cutting-edge research andits application as part of the Scientific Center of Excellence QuantiXLie", PK.1.1.02,European Union, European Regional Development Fund. KK's research is partially supported by MEXT Japan "Leading Initiative for Excellent Young Researchers(LEADER)", JSPS Kakenhi Grant numbers 19KK0065, 21K13775 and 21H04993.DR's research is supported by the Australian Research Council Discovery Project DP210101502 and an Australian Research Council Future Fellowship FT200100431.