Intertwiners of representations of exceptional type quantum affine superalgebras

Abstract

We give explicit formulas for the smallest non-trivial irreducible representation $V$ of quantum affine superalgebras in types D${}_{2|1;\alpha }$, $\dim V=18$ (in the all-fermionic parity), F${}_{3|1}$, $\dim V=41$ (in the distinguished parity), and G${}_{2|1}$, $\dim V=32$ (in the distinguished parity), both in the Drinfeld-Jimbo and in the new Drinfeld realizations. We use this information to obtain an explicit expression for the corresponding $R$-matrices.

Latex, 27 pages, 6 figures