New rational symmetric functions are constructed from the 19-vertex model, with Cauchy identities, stable limits, and a symmetrization formula over 2-permutations.
Construction of $R$-matrices for symmetric tensor representations related to $U_{q}(\widehat{sl_{n}})$
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abstract
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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Rational symmetric functions from the Izergin-Korepin 19-vertex model
New rational symmetric functions are constructed from the 19-vertex model, with Cauchy identities, stable limits, and a symmetrization formula over 2-permutations.