Quantum matrix algebra for the SU(n) WZNW model
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_\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.
Cite
@article{arxiv.hep-th/0003210,
title = {Quantum matrix algebra for the SU(n) WZNW model},
author = {P. Furlan and L. K. Hadjiivanov and A. P. Isaev and O. V. Ogievetsky and P. N. Pyatov and I. T. Todorov},
journal= {arXiv preprint arXiv:hep-th/0003210},
year = {2008}
}
Comments
48 pages, LaTeX, uses amsfonts; final version to appear in J. Phys. A