Relaxed highest-weight modules
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 talk, I shall review relaxed modules and describe how one can rigorously compute their (quite interesting) characters, illustrating this for affine sl(2) and, if time permits, osp(1|2). This proves several conjectural statements in the literature for sl(2), at arbitrary admissible levels, and for osp(1|2) at level −5/4. For other admissible levels, the osp(1|2) results are believed to be new.
[Joint work with Kazuya Kawasetsu, arXiv:1803.01989 [math.RT].]
David Ridout, University of Melbourne