Quantum Affine (Super)Algebras $U_q(A_{1}^{(1)})$ and $U_q(C(2)^{(2)})$

Abstract

We show that the quantum affine algebra $U_{q}(A_{1}^{(1)})$ and the quantum affine superalgebra $U_{q}(C(2)^{(2)})$ admit a unified description. The difference between them consists in the phase factor which is equal to 1 for $U_{q}(A_{1}^{(1)})$ and it is equal to -1 for $U_{q}(C(2)^{(2)})$. We present such a description for the actions of the braid group, for the construction of Cartan-Weyl generators and their commutation relations, as well for the extremal projector and the universal R-matrix. We give also a unified description for the 'new realizations' of these algebras together with explicit calculations of corresponding R-matrices.