Difference equations of quantum current operators and quantum parafermion construction

Details Difference equations of quantum current operators and quantum parafermion construction Difference equations of quantum current operators and quantum parafermion construction

1996-10-18

arxiv.org/abs/q-alg/9610023v1

Mathematics

Quantum Algebra

15 pages Amslatex

Scientific paper

For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we prove that, for the integrable modules of $U_q(\hat {\frak sl}(2))$ of level $k+1$, $x^\pm(z)x^\pm(zq^{\pm 2}) \cdot\cdot\cdot x^\pm(zq^{\pm 2k})$ are vertex operators satisfying certain q-difference equations, and we derive the quantum parafermions of $U_q(\hat {\frak sl}(2))$.

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