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Jordan cells in transfer matrices of finite lattice models are a signature ofthe logarithmic character of the conformal field theories that appear in theirthermodynamical limit. The transfer matrix of periodic loop models, T_N, is anelement of the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha), where Nis the number of sites on a section of the cylinder, and \beta = -(q+1/q) = 2\cos \lambda and \alpha the weights of contractible and non-contractible loops.The thermodynamic limit of T_N is believed to describe a conformal field theoryof central charge c=1-6\lambda^2/(\pi(\lambda-\pi)). The abstract element T_Nacts naturally on (a sum of) spaces V_N^d, similar to those upon which thestandard modules of the (classical) Temperley-Lieb algebra act. These spacesknown as sectors are labeled by the numbers of defects d and depend on a {\emtwist parameter} v that keeps track of the winding of defects around thecylinder. Criteria are given for non-trivial Jordan cells of T_N both betweensectors with distinct defect numbers and within a given sector.

Jordan cells of periodic loop models