Abstract
Orthogonal projections in ℂn ⊗ ℂn of rank one and rank two that give rise to unitary tensor space representations of the Temperley–Lieb algebra TLN(Q) are considered. In the rank one case, a complete classification of solutions is given. In the rank two case, solutions with Q varying in the ranges [2n/3, ∞) and [n/2,∞) are constructed for n = 3k and n = 4k, k ∈ ℕ, respectively.
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