Virasoro algebra and wreath product convolution

TL;DR

This paper introduces a novel group theoretic approach to constructing the Virasoro algebra using wreath products, paralleling geometric methods in Hilbert schemes of points on surfaces.

Contribution

It provides a new algebraic construction of the Virasoro algebra through wreath products, connecting group theory with geometric frameworks.

Findings

Established a wreath product-based construction of the Virasoro algebra

Linked algebraic and geometric perspectives in the theory of Hilbert schemes

Extended the understanding of algebraic structures in geometric contexts

Abstract

We present a group theoretic construction of the Virasoro algebra in the framework of wreath products. This can be regarded as a counterpart of a geometric construction of Lehn in the theory of Hilbert schemes of points on a surface.