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 $U_q({\widehat{\mathfrak{s}l}}_n)$, 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 $U_q({\widehat{\mathfrak{s}l}}_3)$.

AMS-LaTeX, 15pp

References in corpus (4)

• Elliptic quantum groups $E_{\tau ,\eta }(s{l}_2)$ and quasi-Hopf algebras
• Twisting of quantum (super)algebras. Connection of Drinfeld's and Cartan-Weyl realizations for quantum affine algebras
• Zeros and poles of quantum current operators and the condition of quantum integrability
• Singular R-matrices and Drinfeld's comultiplication