Representations and Q-Boson Realization of the Algebra of Functions on the Quantum Group GLq(N)

We present a detailed study of the representations of the algebra of functions on the quantum group $ GL_q(n) $. A q-analouge of the root system is constructed for this algebra which is then used to determine explicit matrix representations of the generators of this algebra. At the end a q-boson realization of the generators of $ GL_q(n) $ is given.