Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\) (Q1308715)

There are known at least four different descriptions of the quantum affine algebra \(U_q(\widehat {\mathfrak g})\): (1) in terms of Chevalley generators by Drinfeld-Jimbo; (2) the so called ``new'' realization by Drinfeld where the whole currents are quantized; (3) in terms of \({\mathcal L}\)-operator by Semenov-Tian-Shansky, Reshetikhin and Frenkel; and (4) in terms of Cartan-Weyl generators by Khoroshkin-Tolstoĭ. Here an explicit isomorphism of the forms (2) and (3) is established for the case of \(U_ q(\widehat {\mathfrak{gl}}_ n)\). More precisely, it is proved that Drinfeld generators are the entries of the Gauss decomposition of the corresponding \(\mathcal L\)-operators.