The quantum Casimir operators of U_q(gl_n) and their eigenvalues

摘要

We show that the quantum Casimir operators of the quantum linear group constructed in early work of Bracken, Gould and Zhang together with one obvious central element generate the entire center of U_q(gl_n). As a byproduct 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.