The representations of the coordinate ring of the quantum symplectic space

In this paper, the irreducible representations of the coordinate ring of quantum symplectic space are classified. Especially, the De Concini–Kac–Procesi conjecture is proved to be true for this algebra. The main steps are the computation of the center and the degree of the algebra by using the associated quasipolynomialalgebra , find some “good” points in the underlying symplectic leaves and construct some quasipolynomial algebras correspond to these “good” points.