Relaxed highest-weight modules II: Classifications for affine vertex algebras

Abstract

This is the second of a series of papers devoted to the study of relaxed highest-weight modules over affine vertex algebras and W-algebras. The first [K. Kawasetsu and D. Ridout, Relaxed highest-weight modules I: Rank 1 cases, Commun. Math. Phys. 368 (2019) 627-663, arXiv:1803.01989 [math.RT]] studied the simple "rank-1"affine vertex superalgebras Lk(2) and Lk((1|2)), with the main results including the first complete proofs of certain conjectured character formulae (as well as some entirely new ones). Here, we turn to the question of classifying relaxed highest-weight modules for simple affine vertex algebras of arbitrary rank. The key point is that this can be reduced to the classification..