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.