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

TL;DR

This paper investigates the algebraic relations of vertex operators in the quantum affine superalgebra $U_q(\\widehat{sl}(M|N))$, demonstrating their representation of the graded Zamolodchikov-Faddeev algebra through bosonization.

Contribution

It provides a detailed analysis of the commutation and invertibility relations of vertex operators for $U_q(\widehat{sl}(M|N))$, highlighting their algebraic structure and similarities between different types.

Findings

Vertex operators realize the graded Zamolodchikov-Faddeev algebra.

Invertibility relations of type-II operators for $N>M$ resemble those of type-I for $M>N$.

Bosonization effectively derives the algebraic relations.

Abstract

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