On Witten multiple zeta-functions associated with semisimple Lie algebras II

Abstract

This is a continuation of our previous result, in which properties of multiple zeta-functions associated with simple Lie algebras of A_r type have been studied. In the present paper we consider more general situation, and discuss the Lie theoretic background structure of our theory. We show a recursive structure in the family of zeta-functions of sets of roots, which can be explained by the order relation among roots. We also point out that the recursive structure can be described in terms of Dynkin diagrams. Then we prove several analytic properties of zeta-functions associated with simple Lie algebras of B_r, C_r, and D_r types.