Quantum spin coverings and statistics

SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail.Comment: 15 page

Photonic Liquid Crystal Fibers with Polymers

Photonic liquid crystal bers with polymers constitute a new solution based on liquid crystals and microstructured polymer optical bers opening up new areas in innovative sensing and photonic devices applications. Compared with their silica-based microstructured bers, it is easier to fabricate exotic microstructured polymer optical bers by extrusion or drilling at low temperature; their nonlinearity is potentially stronger, the range of available polymers that may be drawn is more diverse and the biocompatibility of polymers is often better. Liquid crystals due to their attractive properties i.e., the high birefringence, high electro-optic and thermo-optic eects are a very good candidate for microstructured polymer optical ber inltration to obtain tunable all-in-ber innovative photonic devices. The paper will discuss basic properties and possible applications of the polymer photonic liquid crystal bers that will arise from their high optical tunability with external and internal factors. Current research eort is directed towards two main solutions: photonic crystal bers and microstructured polymer optical ber--based structures, both inltrated with liquid crystals of tailored optical properties