Construction of $R$-matrices for symmetric tensor representations related to $U_q(\widehat{s{l}_n})$

Abstract

In this paper we construct a new factorized representation of the $R$-matrix related to the affine algebra $U_q(\widehat{s{l}_n})$ 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.

arXiv comment19 pages

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Cited by in corpus (17)

• Shift-invariance for vertex models and polymers
• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• A new generalisation of Macdonald polynomials
• Matrix product solution to the reflection equation associated with a coideal subalgebra of $U_q(A_{n-1}^{(1)})$
• An Ising-type formulation of the six-vertex model
• Observables of coloured stochastic vertex models and their polymer limits
• Stochasticization of Solutions to the Yang-Baxter Equation
• Boundary matrices for the higher spin six vertex model
• Hidden diagonal integrability of $q$-Hahn vertex model and Beta polymer model
• Solution of tetrahedron equation and cluster algebras
• Observables of stochastic colored vertex models and local relation
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry
• Integrable Structure of Multispecies Zero Range Process
• $q$-Difference Systems for the Jackson Integral of Symmetric Selberg Type
• Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$