This article is cited in 1 paper

Toward a vertex operator construction of quantum affine algebras

S. E. Klevtsov<sup>ab

a</sup> M. V. Lomonosov Moscow State University
^b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: 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, Serre relations.

Received: 16.01.2006
Revised: 08.08.2007

DOI: 10.4213/tmf6165

 English version: Theoretical and Mathematical Physics, 2008, 154:2, 201–208

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