On the Construction of Trigonometric Solutions of the Yang-Baxter Equation

Abstract

We describe the construction of trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two irreducible representations of a quantum algebra $U_q(\G)$. Our method is a generalization of the tensor product graph method to the case of two different representations. It yields the decomposition of the R-matrix into projection operators. Many new examples of trigonometric R-matrices (solutions to the spectral parameter dependent Yang-Baxter equation) are constructed using this approach.

latex file, 29 pages, Universitaet Bielefeld and University of Queensland preprint, BI-TP-94/13, UQMATH-94-02 (minor correction: in eq. (4.63) the number 32 should be replaced by 36 and in eq. (4.64) -16 becomes -18 and -10 becomes -8.)

References in corpus (8)

• Quantum Inverse Scattering Method and Correlation Functions
• Quantizing SL(N) Solitons and the Hecke Alegbra
• Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters
• Quantum Affine Algebras and Universal $R$-Matrix with Spectral Parameter
• The Analytic Structure of Trigonometric S Matrices
• The full set of $c_n$-invariant factorized $S$-matrices
• On Universal $R$-Matrix for Quantized Nontwisted Rank 3 Affine Lie Algebras
• Quantized Affine Lie Algebras and Diagonalization of Braid Generators

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