The three point gauge algebra $\mathcal{V}⋉\mathfrak{sl}(2,\mathcal{R})\oplus \left({\Omega }_{\mathcal{R}}/d\mathcal{R}\right)$ 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.

arXiv admin note: text overlap with arXiv:1303.6973, arXiv:1502.04102, arXiv:1309.7316