This is the second of a series papers devoted to study relaxed highest-weight modules over affine vertex algebras and W-algebras. The first [K. Kawasetsu D. Ridout, Relaxed I: Rank [Formula: see text] cases, Commun. Math. Phys. 368 (2019) 627–663, arXiv:1803.01989 [math.RT]] studied simple “rank-[Formula: text]” superalgebras text], with main results including complete proofs certain conjecture...

We determine the highest weights that give rise to unitarity when q is real. We further show that when q is on the unit circle and q 6= ±1, then unitary highest weight representations must be finite dimensional and q must be a root of unity. We analyze the special case of the “ladder” representations for su(m,n). Finally we show how the quantized Ladder representations and their analogues for o...

For each r = (r1, r2, . . . , rN ) ∈ C N we construct a highest weight module Mr of the Lie algebra W1+∞. The highest weight vectors are specific tau-functions of the N -th Gelfand–Dickey hierarchy. We show that these modules are quasifinite and we give a complete description of the reducible ones together with a formula for the singular vectors. hep-th/9510211