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Quantum matrix algebra for the SU(n) WZNW model

P. Furlan·L. K. Hadjiivanov·A. P. Isaev·O. V. Ogievetsky·P. N. Pyatov·I. T. Todorov
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Abstract

The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a=(a^i_α) (with noncommuting entries) and by rational functions of n commuting elements q^{p_i}. We study a generalization of the Fock space (F) representation of A for generic q (q not a root of unity) and demonstrate that it gives rise to a model of the quantum universal enveloping algebra U_q(sl_n), each irreducible representation entering F with multiplicity 1. For an integer level k the complex parameter q is an even root of unity, q^h=-1 (h=k+n) and the algebra A has an ideal I_h such that the factor algebra A_h = A/I_h is finite dimensional.

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P. Furlan, L. K. Hadjiivanov, A. P. Isaev, O. V. Ogievetsky, P. N. Pyatov, I. T. Todorov. 2003-04-01. Quantum matrix algebra for the SU(n) WZNW model. https://doi.org/10.1088/0305-4470%2F36%2F20%2F310

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