Solutions of the $U_q({\widehat{\mathfrak{sl}}}_N)$ reflection equations

Abstract

We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type ${\mathrm{A}}_{N-1}^{(1)}$. We also show that all invertible solutions can be obtained by an appropriate affinization procedure from solutions of the constant untwisted and twisted reflection equations.

arXiv comment32 pages; v.2 minor corrections; accepted to J.Phys.A

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Cited by in corpus (5)

• Vertex Models and Spin Chains in Formulas and Pictures
• On the classification of rational K-matrices
• Generic triangular solutions of the reflection equation: $U_q(\widehat{s{l}_2})$ case
• Reflection $K$ matrices associated with an Onsager coideal of $U_p(A_{n-1}^{(1)})$, $U_p(B_n^{(1)})$, $U_p(D_n^{(1)})$ and $U_p(D_{n+1}^{(2)})$
• Reflection Maps Associated with Involutions and Factorization Problems, and Their Poisson Geometry