We show that the quantum Casimir operators of the quantum linear group
constructed in early work of Bracken, Gould and Zhang together with one extra
central element generate the entire center of $\Uq$. As a by product of the
proof, we obtain intriguing new formulae for eigenvalues of these quantum
Casimir operators, which are expressed in terms of the characters of a class of
finite dimensional irreducible representations of the classical general linear
algebra.