  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 $TL_N(\sqrt n)$.
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
