SOLUTIONS OF THE QUANTUM YANG-BAXTER EQUATION WITH EXTRA NONADDITIVE PARAMETERS

We present a systematic technique to construct solutions to the Yang-B axter equation which depend not only on a spectral parameter but in ad dition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter bu t in a non-additive form. We exploit the fact that quantum non-compact algebras such as U(q)(su(1, 1)) and type-I quantum superalgebras such as U(q)(gl(1/1)) and U(q)(gl(2/1)) are known to admit non-trivial one -parameter families of infinite-dimensional and finite-dimensional irr eps, respectively, even for generic q. We develop a technique for cons tructing the corresponding spectral-dependent R-matrices. As examples, we work out the the R-matrices for the three quantum algebras mention ed above in certain representations.