Vertex Operators of the $q$-Virasoro Algebra; Defining Relations,   Adjoint Actions and Four Point Functions
  Primary fields of the $q$-deformed Virasoro algebra are constructed. Commutation relations among the primary fields are studied. Adjoint actions of the deformed Virasoro current on the primary fields are represented by the shift operator $\Theta_{\xi} f(x)=f(\xi x)$. Four point functions of the primary fields enjoy the connection formula associated with the Boltzmann weights of the fusion Andrews-Baxter-Forrester model. 
H. Awata, H. Kubo, Y. Morita, S. Odake and J. Shiraishi