Temperley-Lieb R-matrices from generalized Hadamard matrices
Jean Avan, Tiago Fonseca, Luc Frappat, Petr Kulish, Eric Ragoucy and, Genevieve Rollet
TL;DR
This paper introduces new rank n-representations of the Temperley-Lieb algebra using matrices that generalize complex Hadamard matrices, providing classifications including Fourier and Butson matrices.
Contribution
It constructs novel representations of the Temperley-Lieb algebra based on generalized Hadamard matrices and offers partial classifications of these matrices.
Findings
New rank n-representations of TL_N(q) constructed
Characterization of matrices generalizing complex Hadamard property
Partial classification including Fourier and Butson matrices
Abstract
New sets of rank n-representations of Temperley-Lieb algebra TL_N(q) are constructed. They are characterized by two matrices obeying a generalization of the complex Hadamard property. Partial classifications for the two matrices are given, in particular when they reduce to Fourier or Butson matrices.
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