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

TL;DR

This paper explores Virasoro-type reductions and inverse reductions for W-algebras linked to classical Lie types and nilpotent orbits, extending these concepts to universal vertex algebras.

Contribution

It establishes new reduction and inverse reduction techniques for W-algebras and lifts these results to universal vertex algebra objects.

Findings

Virasoro-type reductions for W-algebras are established.

Inverse reductions corresponding to these are constructed.

Results are extended to universal vertex 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 $\mathcal{W}^{\mathfrak{sp}}_{\infty}$.