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

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 $T{L}_N(Q)$ 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.

19 pages, LaTex

References in corpus (2)

• Temperley-Lieb R-matrices from generalized Hadamard matrices
• Tensor space representations of Temperley-Lieb algebra via orthogonal projections of rank $r\ge 1$

Cited by in corpus (2)

• Yang-Baxter representations of the infinite symmetric group
• Tensor space representations of Temperley-Lieb algebra via orthogonal projections of rank $r\ge 1$