Reflection matrices from Hadamard-type Temperley-Lieb R-matrices

We classify non-operatorial matrices K solving Skylanin’s quantum reflection equation for all R-matrices obtained from the newly defined general rank- n Hadamard type representations of the Temperley-Lieb algebra $T{L}_N(\sqrt{n})$. They are characterized by a universal set of algebraic equations in a specific canonical basis uniquely defined from the “Master matrix” associated to the chosen realization of Temperley-Lieb algebra