The elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ and its bosonization at level one

Details The elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ and its bosonization at level one The elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ and its bosonization at level one

1997-04-03

arxiv.org/abs/hep-th/9704024v2

J.Math.Phys. 39 (1998) 4356-4368

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, Latex file 43k

Scientific paper

10.1063/1.532539

We extend the work of Foda et al and propose an elliptic quantum algebra $A_{q,p}(\hat {sl_n})$. Similar to the case of $A_{q,p}(\hat {sl_2})$, our presentation of the algebra is based on the relation $RLL=LLR^*$, where $R$ and $R^*$ are $Z_n$ symmetric R-matrices with the elliptic moduli chosen differently and a factor is also involved. With the help of the results obtained by Asai et al, we realize type I and type II vertex operators in terms of bosonic free fields for $Z_n$ symmetric Belavin model. We also give a bosonization for the elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ at level one.

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