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

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

1993-05-26

arxiv.org/abs/hep-th/9305146v1

Commun.Math.Phys. 162 (1994) 61-84

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, LaTeX, RIMS-924, YITP/K-1018

Scientific paper

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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