Bulg. J. Phys. vol.40 no.2 (2013), pp. 141-146

SU(n) WZNW fusion and a Q-algebra

L. Hadjiivanov1, P. Furlan2
1Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria
2Dipartimento di Fisica dell' Università degli Studi di Trieste, I-34014 Trieste and Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, Italy
Abstract. The quantum group covariant quantization of the chiral parts of the Wess-Zumino-Novikov-Witten (WZNW) model on a compact Lie group G gives rise to an extension of the 2D unitary model involving matrix algebras (with non-commutative entries) generated by chiral "zero modes" aiα, āβj. The quantum group invariant combinations of the latter Qij = aiα ⊗ āαj represent the internal symmetry of the model in a setting that generalizes the axiomatic approach to gauge theories. Here we sketch the concept of the Q-operators for G = SU(n) starting with n = 2 outline the steps to follow for arbitrary n and discuss the relation of the Q-algebra with the WZNW fusion.

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