INFINITE FAMILIES OF GAUGE-EQUIVALENT R-MATRICES AND GRADATIONS OF QUANTIZED AFFINE ALGEBRAS

Associated with the fundamental representation of a quantum algebra su ch as U(q)(A1) or U(q)(A2), there exist infinitely many gauge-equivale nt R-matrices with different spectral-parameter dependences. It is sho wn how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as U(q) (A1(1)) and U(q)(A2(1)), and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relat e the R-matrices in different gradations. Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.