Construction of R-matrices for symmetric tensor representations related to Uq (sln )

Gary Bosnjak; Vladimir V. Mangazeev

doi:10.1088/1751-8113/49/49/495204

Construction of R-matrices for symmetric tensor representations related to U_q (sl_n )

Gary Bosnjak
, Vladimir V. Mangazeev

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

Abstract

In this paper we construct a new factorized representation of the R-matrix related to the affine algebra 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.

Original language	English
Article number	495204
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	49
Issue number	49
DOIs	https://doi.org/10.1088/1751-8113/49/49/495204
Publication status	Published - 21 Nov 2016

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10.1088/1751-8113/49/49/495204

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abstract = "In this paper we construct a new factorized representation of the R-matrix related to the affine algebra 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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N2 - In this paper we construct a new factorized representation of the R-matrix related to the affine algebra 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.

AB - In this paper we construct a new factorized representation of the R-matrix related to the affine algebra 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.

KW - Yang-Baxter equation

KW - integrable systems

KW - quantum algebras

UR - https://www.scopus.com/pages/publications/84999853104

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Construction of R-matrices for symmetric tensor representations related to U_q (sl_n )

Abstract

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