The vertex operators

Abstract

The vertex operators are the most important objects in representation theory of quantum groups. They are defined as certain intertwining operators of quantum group modules. In this chapter, we discuss the vertex operators of the Uq,p(sl2) -modules. There are two types of them, type I and II, due to an asymmetry of the comultiplication with respect to the tensor components. By using the evaluation representation and the level-1 highest weight representation constructed in the last chapter, we solve the intertwining relations and obtain a realization of the vertex operators explicitly. Exchange relations among the vertex operators are also given. Thus obtained vertex operators become a key to the rest of this book.