On quantum group symmetries of conformal field theories
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hep-th
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quantumsymmetriesconformalgroupstheorychiralclassicalfield
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The appearance of quantum groups in conformal field theories is traced back to the Poisson-Lie symmetries of the classical chiral theory. A geometric quantization of the classical theory deforms the Poisson-Lie symmetries to the quantum group ones. This elucidates the fundamental role of chiral symmetries that quantum groups play in conformal models. As a byproduct, one obtains a more geometric approach to the representation theory of quantum groups.
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