A coset-type construction for the deformed Virasoro algebra

TL;DR

This paper constructs analogs of minimal unitary series representations for the deformed Virasoro algebra using vertex operators from quantum affine and elliptic algebras, advancing the understanding of their structure.

Contribution

It introduces a new construction method for the deformed Virasoro algebra representations via vertex operators from quantum and elliptic algebras.

Findings

Constructed analogs of minimal unitary series for the deformed Virasoro algebra.

Proposed a similar construction for the elliptic algebra $A_{q,p}(\

Abstract

An analog of the minimal unitary series representations for the deformed Virasoro algebra is constructed using vertex operators of the quantum affine algebra $U_q(\hat{sl}_2)$. A similar construction is proposed for the elliptic algebra $A_{q,p}(\hat{sl}_2)$.