In this paper we construct a new factorized representation of the R-matrix related to the affine algebra U q ( sl n ) for symmetric tensor representations with arbitrary weights. Using the 3D approach we obtain explicit formulas for the matrix elements of the R-matrix and give a simple proof that a "twisted" R-matrix is stochastic. We also discuss symmetries of the R-matrix, its degenerations and compare our formulas with other results available in the literature.

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