Construction of $R$-matrices for symmetric tensor representations related to $U_{q}(\widehat{sl_{n}})$

Gary Bosnjak; Vladimir V. Mangazeev

Construction of R-matrices for symmetric tensor representations related to U_(q)(widehat{sl_(n)})

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arxiv 1607.07968 v1 pith:276WMPA4 submitted 2016-07-27 math-ph hep-thmath.MPmath.QA

Construction of R-matrices for symmetric tensor representations related to U_(q)(widehat{sl_(n)})

Gary Bosnjak , Vladimir V. Mangazeev This is my paper

classification math-ph hep-thmath.MPmath.QA

keywords matrixformulasrelatedrepresentationssymmetrictensorwidehataffine

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In this paper we construct a new factorized representation of the $R$-matrix related to the affine algebra $U_{q}(\widehat{sl_{n}})$ 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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