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.

19 pages

References in corpus (3)

• Quantum geometry of 3-dimensional lattices
• Q-operators in the six-vertex model
• On the universal R-matrix for the Izergin-Korepin model

Cited by in corpus (5)

• An Ising-type formulation of the six-vertex model
• Boundary matrices for the higher spin six vertex model
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$
• Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation