In my talk, I will introduce several sets of central elements in the universal enveloping algebra U(gl_N) and explain the relationships between them using average value of the gl-weight system as an example. As a consequence, we obtain a proof of the M.Kazarian, E.Krasilnikov, S.Lando, and M.Shapiro conjecture that the mean value of the gl-weight system is a tau function of the KP hierarchy.