G-equivariant ϕ-coordinated quasi modules for quantum vertex algebras

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-equivariant ϕ-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-equivariant ϕ-coordinated quasi modules. As an illustrating example, we study a special case of the deformed Virasoro algebra \documentclass[12pt]{minimal}\begin{document}${\mathcal {V}}ir_{p,q}$\end{document}Virp,q with q = −1, to which we associate a Clifford vertex superalgebra and its G-equivariant ϕ-coordinated quasi modules.