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.

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