Subregular W-algebras of type A

Abstract

Subregular W-algebras are an interesting and increasingly important class of quantum hamiltonian reductions of affine vertex algebras. Here, we show that the [Formula: see text] subregular W-algebra can be realized in terms of the [Formula: see text] regular W-algebra and the half lattice vertex algebra [Formula: see text]. This generalizes the realizations found for [Formula: see text] and [Formula: see text] in [D. Adamović, Realizations of simple affine vertex algebras and their modules: The cases [Formula: see text] and [Formula: see text], Comm. Math. Phys. 366 (2019) 1025–1067, arXiv:1711.11342 [math.QA]; D. Adamović, K. Kawasetsu and D. Ridout, A realization of the Bershadsky–Polyakov algebras and their relaxed modules, Lett. Math. Phys., 111 (2021) 1–30, arXiv:2007.00396 [math.QA]] and can be interpreted as an inverse quantum hamiltonian reduction in the sense of Adamović. We use this realization to explore the representation theory of [Formula: see text] subregular W-algebras. Much of the structure encountered for [Formula: see text] and [Formula: see text] is also present for [Formula: see text]. Particularly, the simple [Formula: see text] subregular W-algebra at nondegenerate admissible levels can be realized purely in terms of the [Formula: see text] minimal model vertex algebra and [Formula: see text].