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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

Gary Bosnjak , Vladimir V. Mangazeev This is my paper · ORCID
classification math-phhep-thmath.MPmath.QA
keywords matrixformulasrelatedrepresentationssymmetrictensorwidehataffine
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Rational symmetric functions from the Izergin-Korepin 19-vertex model

    math.CO 2024-12 conditional novelty 7.0 of 10

    New rational symmetric functions are constructed from the 19-vertex model, with Cauchy identities, stable limits, and a symmetrization formula over 2-permutations.

  2. The boundary-driven multispecies harmonic process

    math-ph 2026-07 conditional novelty 6.0 of 10

    A multispecies harmonic process with boundary reservoirs is introduced and proven Yang-Baxter integrable via a factorized R-matrix and open-chain K-matrices, with three dual processes.

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