Twisted and Non-Twisted Deformed Virasoro Algebra via Vertex Operators of $U_q(\widehat{\mathfrak{sl}}_2)$

Abstract

The work is devoted to a probably new connection between deformed Virasoro algebra and quantum $\widehat{\mathfrak{sl}}_2$. We give an explicit realization of Virasoro current via vertex operators of level 1 integrable representation of $\widehat{\mathfrak{sl}}_2$. The same is done for a twisted version of deformed Virasoro algebra.