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arXiv · 1505.02703

Tensor space representations of Temperley-Lieb algebra and generalized permutation matrices

Andrei Bytsko
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Abstract

Orthogonal projections in ${\mathbb C}^n \otimes {\mathbb C}^n$ of rank one and rank two that give rise to unitary tensor space representations of the Temperley-Lieb algebra $TL_N(Q)$ 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 $[2n/3,\infty)$ and $[n/\sqrt{2},\infty)$ are constructed for $n=3k$ and $n=4k$, $k \in {\mathbb N}$, respectively.

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Andrei Bytsko. 2015-10-18. Tensor space representations of Temperley-Lieb algebra and generalized permutation matrices. https://doi.org/10.1063/1.4927631

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