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arXiv:1607.07968 · Journal of Physics A Mathematical and Theoretical

Construction of R -matrices for symmetric tensor representations related to U q ( sl n ˆ )

Gary Bosnjak, Vladimir V. Mangazeev

Published Nov 21, 2016• 28 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
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 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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We describe the twisted affine superalgebra and its quantized version . We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point subsuperalgebra . We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two invariant R-matrices: one of them corresponds to and the other to . Using the R-matrix for , we construct a new invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger symmetry.