Zeta-functions of weight lattices of compact connected semisimple Lie groups

Author:

Yasushi~Komori,~Kohji~Matsumoto,~Hirofumi~Tsumura

2010 Mathematics Subject Classification:

11M41, 11M32, 17B20, 40B05.

Keywords:

Lie group, multiple zeta values, root systems, Witten's zeta-functions.

Abstract:

We define zeta-functions of weight lattices of compact connected semisimple Lie groups. If the group is simply-connected, these zeta-functions coincide with ordinary zeta-functions of root systems of associated Lie algebras. In this paper, we consider the general connected (but not necessarily simply-connected) case, prove the explicit form of Witten's volume formulas for these zeta-functions, and further prove functional relations among them which include their volume formulas. Also, we give new examples of zeta-functions for which parity results hold.

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Vol. 10 (18), 2015