On Virasoro-type reductions and inverse Hamiltonian reductions for $W$-algebras and $W_\infty$-algebras

Abstract

In this article, the Virasoro-type reduction and the corresponding inverse reductions are established for W-algebras associated with classical Lie type and nilpotent orbits of height two. Moreover, these results are lifted to the universal objects by analyzing the Virasoro-type reduction of the vertex algebra $\mathcal{W}^{\mathfrak{sp}}_{\infty}$.