On the FRTS approach to quantized current algebras

Abstract

We study the possibility to establish $L$-operator's formalism by Faddeev-Reshetikhin-Takhtajan-Semenov-Tian-Shansky (FRST) for quantized current algebras, that is, for quantum affine algebras in the ''new realization '' by V. Drinfeld with the corresponding Hopf algebra structure and for their Yangian counterpart. We establish this formalism using the twisting procedure by Tolstoy and the second author and explain the problems which FRST approach encounter for quantized current algebras. We show also that, for the case of $U_q(\hat {\frak sl}_n)$, entries of the L-operators of FRTS type give the Drinfeld current operators for the non-simple roots, which we discovered recently. As an application we deduce the commutation relations between these current operators for $U_q(\hat {\frak sl}_3)$.