UNIFIED DESCRIPTION OF QUANTUM AFFINE (SUPER)ALGEBRAS $U_{q}(A_{1}^{(1)})$ AND Uq(C(2)(2))

Abstract

We show that the quantum affine algebra U_{q}(A_{1}^{(1)}) and the quantum affine superalgebra U_{q}(C(2)^{(2)}) admit unified description. The difference between them consists in the phase factor which is equal to 1 for U_{q}(A_{1}^{(1)}) and is equal to -1 for U_{q}(C(2)^{(2)}). We present such a description for the construction of Cartan-Weyl generators and their commutation relations, as well for the universal R-matrices.