Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $A_{n-1}^{(1)}$

Abstract

A trick to obtain a systematic solution to the set-theoretical reflection equation is presented from a known one to the Yang-Baxter equation. Examples are given from crystals and geometric crystals associated to the quantum affine algebra of type $A_{n-1}^{(1)}$.

7 pages, minor modifications

References in corpus (2)

• Set-theoretical reflection equation: Classification of reflection maps
• Matrix product solution to the reflection equation associated with a coideal subalgebra of $U_q(A_{n-1}^{(1)})$

Cited by in corpus (5)

• Boundary from bulk integrability in three dimensions: 3D reflection maps from tetrahedron maps
• Reflection equation as a tool for studying solutions to the Yang-Baxter equation
• Second-order Symmetric Non-negative Latent Factor Analysis
• Reflections to set-theoretic solutions of the Yang-Baxter equation
• Reflection Maps Associated with Involutions and Factorization Problems, and Their Poisson Geometry