A Classically Singular Representation of su_q(n)

A \rep of \sun, which diverges in the limit of \cl, is investigated. This is an infinite dimensional and a non-unitary \rep, defined for the real value of $ q, \ 0 < q < 1. $ Each \irrep is specified by $ n $ continuous variables and one discrete variable. This \rep gives a new solution of the Yang-Baxter equation, when the R-matrix is evaluated. It is shown that a continuous variables can be regarded as a spectral parameter.