THE ELLIPTIC QUANTUM ALGEBRA A(Q),(P)(SL(N)) AND ITS BOSONIZATION AT LEVEL ONE

We extend the work of Foda et al. and propose an elliptic quantum alge bra A(q,p)(<(sl(n))over cap>). Similar to the case of A(q,p)(<(sl(n))o ver cap>), our presentation of the algebra is based on the relation RL L=LLR, where A and R* are Z(n) symmetric A matrices with the elliptic moduli chosen differently, and a scalar factor is also involved. With the help of the results obtained by Asai et al., we realize type I an d type II vertex operators in terms of bosonic free fields for the Z(n ) symmetric Belavin model. We also give a bosonization for the ellipti c quantum algebra A(q,p)(<(sl(n))over cap>) at level one. (C) 1998 Ame rican Institute of Physics.