5 research outputs found
Quantum matrix algebra for the SU(n) WZNW model
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.Comment: 48 pages, LaTeX, uses amsfonts; final version to appear in J. Phys.