The three point gauge algebra $\mathcal V\ltimes \mathfrak{sl}(2, \mathcal R) \oplus\left(\Omega_{\mathcal R}/d{\mathcal R}\right)$ and an action on a Fock space

Abstract

The three point current algebra $\mathfrak{sl}(2,\mathcal R)$ where $\mathcal R=\mathbb C[t,t^{-1},u\,|\,u^2=t^2+4t ]$ and three-point Virasoro algebra both act on a previously constructed Fock space. In this paper we prove that the semi-direct product, i.e. the gauge algebra acts on the Fock space as well.