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Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{{\mathfrak g}{\mathfrak l}(n)})\). (English) Zbl 0786.17008
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-Tolstoj.
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.

17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
Full Text: DOI
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