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We consider commutation relations and invertibility relations of vertexoperators for the quantum affine superalgebra $U_q(\widehat{sl}(M|N))$ by usingbosonization. We show that vertex operators give a representation of the gradedZamolodchikov-Faddeev algebra by direct computation.Invertibility relations oftype-II vertex operators for $N>M$ are very similar to those of type-I for$M>N$.

Commutation relations of vertex operators for $U_q(\widehat{sl}(M|N))$