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arXiv · hep-th/9305146

Free Boson Realization of $U_q(\widehat{sl_N})$

H. Awata·S. Odake·J. Shiraishi
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Abstract

We construct a realization of the quantum affine algebra $U_q(\widehat{sl_N})$ of an arbitrary level $k$ in terms of free boson fields. In the $q\!\rightarrow\! 1$ limit this realization becomes the Wakimoto realization of $\widehat{sl_N}$. The screening currents and the vertex operators(primary fields) are also constructed; the former commutes with $U_q(\widehat{sl_N})$ modulo total difference, and the latter creates the $U_q(\widehat{sl_N})$ highest weight state from the vacuum state of the boson Fock space.

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H. Awata, S. Odake, J. Shiraishi. 1993-05-26. Free Boson Realization of $U_q(\widehat{sl_N})$. https://doi.org/10.1007/bf02105187

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