Temperley-Lieb R-matrices from generalized Hadamard 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.

17 pages

References in corpus (2)

• Construction, classification and parametrization of complex Hadamard matrices
• Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices

Cited by in corpus (5)

• Tensor space representations of Temperley-Lieb algebra and generalized permutation matrices
• Tensor space representations of Temperley-Lieb algebra via orthogonal projections of rank $r\ge 1$
• Isolated partial Hadamard matrices, and related topics
• Reflection matrices from Hadamard-type Temperley-Lieb R-matrices
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish