## Journal of the Mathematical Society of Japan

### 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 Ar 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 Br, Cr, and Dr types.

#### Article information

Source
J. Math. Soc. Japan Volume 62, Number 2 (2010), 355-394.

Dates
First available in Project Euclid: 7 May 2010

http://projecteuclid.org/euclid.jmsj/1273236709

Digital Object Identifier
doi:10.2969/jmsj/06220355

Zentralblatt MATH identifier
05725848

Mathematical Reviews number (MathSciNet)
MR2662849

#### Citation

KOMORI, Yasushi; MATSUMOTO, Kohji; TSUMURA, Hirofumi. On Witten multiple zeta-functions associated with semisimple Lie algebras II. Journal of the Mathematical Society of Japan 62 (2010), no. 2, 355--394. doi:10.2969/jmsj/06220355. http://projecteuclid.org/euclid.jmsj/1273236709.

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