Solutions of the quantum Yang-Baxter equation with extra nonadditive parameters

Abstract

We present a systematic technique to construct solutions to the Yang-Baxter\nequation which depend not only on a spectral parameter but in addition on\nfurther continuous parameters. These extra parameters enter the Yang-Baxter\nequation in a similar way to the spectral parameter but in a non-additive form.\nWe exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$\nand type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are\nknown to admit non-trivial one-parameter families of infinite-dimensional and\nfinite dimensional irreps, respectively, even for generic $q$. We develop a\ntechnique for constructing the corresponding spectral-dependent R-matrices. As\nexamples we work out the the $R$-matrices for the three quantum algebras\nmentioned above in certain representations.\n