Journal article
Classifying Relaxed Highest-Weight Modules for Admissible-Level Bershadsky–Polyakov Algebras
Z Fehily, K Kawasetsu, D Ridout
Communications in Mathematical Physics | SPRINGER | Published : 2021
Abstract
The Bershadsky–Polyakov algebras are the minimal quantum hamiltonian reductions of the affine vertex algebras associated to sl3 and their simple quotients have a long history of applications in conformal field theory and string theory. Their representation theories are therefore quite interesting. Here, we classify the simple relaxed highest-weight modules, with finite-dimensional weight spaces, for all admissible but nonintegral levels, significantly generalising the known highest-weight classifications (Arakawa in Commun Math Phys 323:627–633, 2013, Adamović and Kontrec in Classification of irreducible modules for Bershadsky–Polyakov algebra at certain levels). In particular, we prove that..
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Awarded by Australian Research Council
Funding Acknowledgements
We thank Draen Adamovi, Tomoyuki Arakawa and Thomas Creutzig for interesting discussions related to the research reported here. ZF's research is supported by an Australian Government Research Training Program (RTP) Scholarship. 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.