$G$-covariant $\phi$-coordinated quasi modules for quantum vertex algebras

TL;DR

This paper introduces new concepts of T-type quantum vertex algebras and G-covariant phi-coordinated quasi modules, extending previous results and analyzing a deformed Virasoro algebra case with Clifford superalgebra connections.

Contribution

It defines T-type quantum vertex algebras and G-covariant phi-coordinated quasi modules, providing a commutator formula and applying it to a specific deformed Virasoro algebra case.

Findings

Refined and extended previous results on quantum vertex algebras.

Derived a commutator formula for G-covariant phi-coordinated quasi modules.

Studied a special case involving the deformed Virasoro algebra and Clifford vertex superalgebra.

Abstract

This is a paper in a series to study quantum vertex algebras and their relations with various quantum algebras. In this paper, we introduce a notion of T-type quantum vertex algebra and a notion of $G$-covariant $\phi$-coordinated quasi module for a $T$-type quantum vertex algebra with an automorphism group $G$. We refine and extend several previous results and we obtain a commutator formula for $G$-covariant $\phi$-coordinated quasi modules. As an illustrating example, we study a special case of the deformed Virasoro algebra $\V_{p,q}$ with $q=-1$, to which we associate a Clifford vertex superalgebra and its $G$-covariant $\phi$-coordinated quasi modules.