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×n matrix a = (aα) , i, α = 1, . . . , n (with noncommuting entries) and by rational functions of n commuting elements qi satisfying n ∏ i=1 qi = 1, qaα = a j αq pi+δ j i− 1 n . 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 Uq = Uq(sln) each irreducible representation entering F with multiplicity 1 . For an integer ŝu(n) height h(= k + n ≥ n) the complex parameter q is an even root of unity, q = −1 , and the algebra A has an ideal Ih such that the factor algebra Ah = A/Ih is finite dimensional. All physical Uq modules – of shifted weights satisfying p1n ≡ p1 − pn < h – appear in the Fock representation of Ah .