Zetafunctions of weight lattices of compact connected semisimple Lie groups
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2010 Mathematics Subject Classification:

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

Keywords:

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

Abstract:

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

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Vol. 10 (18), 2015
