The Center of the Quantized Matrix Algebra

We compute the center in the case where q is a root of unity. Main steps are to compute the degree of an associated quasipolynomial algebra and to compute the dimensions of some interesting irreducible modules. 1. Introduction Quantum groups arose from a quantum mechanical problem in statistical mechanics , the quantum Yang-Baxter equation (QYBE). Following Drinfeld 5], a quantum group is the dual of a Hopf algebra and a quantum aane space is the dual of an associative algebra. This algebra is called the coordinate algebra of the quantum aane space. In 11] and 12], a quantum matrix space M q (n) was deened which can be viewed as a deformation of the full matrix algebra M n (C). The coordinate algebra