## Abstract

Jordan cells in transfer matrices of finite lattice models are a signature of the logarithmic character of the conformal field theories that appear in their thermodynamical limit. The transfer matrix of periodic loop models, T _{N}, is an element of the periodic Temperley-Lieb algebra , where N is the number of sites on a section of the cylinder, and β = -q - q ^{-1} = 2cos λ and the weights of contractible and non-contractible loops. The thermodynamic limit of T_{N} is believed to describe a conformal field theory of central charge c = 1 - 6λ ^{2}/(π(λ - π)). The abstract element T_{N} acts naturally on (a sum of) spaces , similar to those upon which the standard modules of the (classical) Temperley-Lieb algebra act. These spaces known as sectors are labeled by the numbers of defects d and depend on a twist parameter v that keeps track of the winding of defects around the cylinder. Criteria are given for non-trivial Jordan cells of T_{N} both between sectors with distinct defect numbers and within a given sector.

Original language | English |
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Article number | 494013 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 46 |

Issue number | 49 |

DOIs | |

Publication status | Published - 13 Dec 2013 |

Externally published | Yes |