Quantum Generalized Projective Representation Of Type A

To begin with, this paper realizes the quantized universal enveloping algebra Uq(sln+1) as certain quantum differential operators in Wq(2n) defined over the quantum divided power algebra Aq(n). Next, the paper gives a construction of a representation of Uq(sln+1) on Aq(n)(?)V, that is, the so called quantum generalized projective representation of Uq(sln+1), where V is an arbitrary finite dimensional irreducible Uq(gln)- module. Finally, we get a necessary and sufficient condition for the irreducibility of this repre-sentation in the special of n=2,q is not a root of unity. In particular, we obtain a new family infinite dimensional irreducible Uq(sl3)- modules, which are in general not highest weight modules.