Journal article
Relaxed Highest-Weight Modules I: Rank 1 Cases
K Kawasetsu, D Ridout
Communications in Mathematical Physics | SPRINGER | Published : 2019
Abstract
Relaxed highest-weight modules play a central role in the study of many important vertex operator (super)algebras and their associated (logarithmic) conformal field theories, including the admissible-level affine models. Indeed, their structure and their (super)characters together form the crucial input data for the standard module formalism that describes the modular transformations and Grothendieck fusion rules of such theories. In this article, character formulae are proved for relaxed highest-weight modules over the simple admissible-level affine vertex operator superalgebras associated to sl 2 and osp(1 | 2). Moreover, the structures of these modules are specified completely. This prove..
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Awarded by Australian Research Council
Funding Acknowledgements
We thank Drazen Adamovic, Tomoyuki Arakawa, Thomas Creutzig, Tianshu Liu, and SimonWood for useful discussions as well as their encouragement. We also thank Will Stewart for pointing out a small error in a previous version and Ryo Sato for clarifying for us the relation between his work and relaxed sl<INF>2</INF>-characters. KK's research is supported by the 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.