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 ${\mathcal{W}}_{\infty }^{\mathfrak{sp}}$.

40 pages, section 9 on Virasoro reduction for universal W-algebras has been added