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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 $A_{q,p}(\hat {sl_2})$, ourpresentation of the algebra is based on the relation $RLL=LLR^*$, where $R$ and$R^*$ are $Z_n$ symmetric R-matrices with the elliptic moduli chosendifferently and a factor is also involved. With the help of the resultsobtained by Asai et al, we realize type I and type II vertex operators in termsof bosonic free fields for $Z_n$ symmetric Belavin model. We also give abosonization for the elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ at levelone.Comment: 17 pages, Latex file 43

The elliptic quantum algebra Aq,p(sln∧) and its bosonization at level one