Bosonization and vertex operator of supersymmetry $u_q(\widehat{sl}(n\mathrm{\mid }1))$ for level $k$

We construct a bosonization of the quantum superalgebra $U_q(\widehat{sl}(N\mathrm{\mid }1))$ for an arbitrary level $k$. We construct the screening that commutes with the quantum superalgebra for an arbitrary level $k\mathrm{\ne }-N+1$. We propose a bosonization of the vertex operator that gives the intertwiner among the Wakimoto realization and the typical representation.