Set-theoretical reflection equation: Classification of reflection maps
  The set-theoretical reflection equation and its solutions, the reflection maps, recently introduced by two of the authors, is presented in general and then applied in the context of quadrirational Yang-Baxter maps. We provide a method for constructing reflection maps and we obtain a classification of solutions associated to all the families of quadrirational Yang-Baxter maps that have been classified recently. 
V. Caudrelier, N. Crampe, Q.C. Zhang
math-ph hep-th math.MP math.QA nlin.SI