Geodesic
Toward a vertex operator construction of quantum affine algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 240-248

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We describe a construction of the quantum-deformed affine algebras using vertex operators in the free field theory. We prove the Serre relations for the Borel subalgebras of quantum affine algebras; in particular, we consider the $\widehat{sl}_2$ case in detail. We also construct the generators corresponding to the positive roots of $\widehat{sl}_2$.
Keywords: quantum group, quantum affine algebra, free field theory, minimal model
Mots-clés : Serre relations. 
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     author = {S. E. Klevtsov},
     title = {Toward a vertex operator construction of quantum affine algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {240--248},
     publisher = {mathdoc},
     volume = {154},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a2/}
}
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S. E. Klevtsov. Toward a vertex operator construction of quantum affine algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 240-248. http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a2/