Vertex Operators of $U_q[\hat{gl(N|N)}]$ and Highest Weight Representations of $U_q[\hat{gl(2|2)}]$

Abstract

We determine the exchange relations of the level-one q-vertex operators of the quantum affine superalgebra $U_q[\hat{gl(N|N)}]$. We study in details the level-one irreducible highest weight representations of $U_q[\hat{gl(2|2)}]$, and compute the characters and supercharacters associated with these irreducible modules.