Quantum matrix algebra for the SU(n) WZNW model

Details Quantum matrix algebra for the SU(n) WZNW model Quantum matrix algebra for the SU(n) WZNW model

2000-03-23

arxiv.org/abs/hep-th/0003210v4

J.Phys.A36:5497-5530,2003

Physics

High Energy Physics

High Energy Physics - Theory

48 pages, LaTeX, uses amsfonts; final version to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/36/20/310

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_\alpha) (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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