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 α ), i, α = 1,....,n (with noncommuting entries) and by rational functions of n commuting elements q P 1 satisfying Π n i = 1 q p i = 1, q p i a j α = a j α q p i + δ j 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 = U q (sl n ), with each irreducible representation entering F with multiplicity 1. For an integer su (n) height h (= k + n ≥ n) the complex parameter q is an even root of unity, q h = -1, and the algebra A has an ideal I h such that the factor algebra A n = A/I h is finite dimensional. All physical Uq modules-of shifted weights satisfying p 1 n ≡ p 1 - p n < h-appear in the Fock representation of A h .