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.

22 pages, LaTeX

References in corpus (1)

• Twisting of quantum (super)algebras. Connection of Drinfeld's and Cartan-Weyl realizations for quantum affine algebras

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