Solutions of the $U_q(\widehat{\mathfrak{sl}}_N)$ reflection equations
Vidas Regelskis, Bart Vlaar
TL;DR
This paper classifies all invertible solutions to the reflection equations associated with the Bazhanov-Jimbo R-matrix for type A^{(1)}_{N-1}, demonstrating they can be derived from constant solutions via affinization.
Contribution
It provides a complete classification of invertible solutions to both untwisted and twisted reflection equations for a specific quantum affine algebra.
Findings
All invertible solutions are obtained through affinization of constant solutions.
The solutions cover both untwisted and twisted reflection equations.
The classification applies to the Bazhanov-Jimbo R-matrix of type A^{(1)}_{N-1}.
Abstract
We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type . 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra