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April, 2010 On Witten multiple zeta-functions associated with semisimple Lie algebras II
Yasushi KOMORI, Kohji MATSUMOTO, Hirofumi TSUMURA
J. Math. Soc. Japan 62(2): 355-394 (April, 2010). DOI: 10.2969/jmsj/06220355

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.

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Yasushi KOMORI. Kohji MATSUMOTO. Hirofumi TSUMURA. "On Witten multiple zeta-functions associated with semisimple Lie algebras II." J. Math. Soc. Japan 62 (2) 355 - 394, April, 2010. https://doi.org/10.2969/jmsj/06220355

Information

Published: April, 2010
First available in Project Euclid: 7 May 2010

zbMATH: 1210.11099
MathSciNet: MR2662849
Digital Object Identifier: 10.2969/jmsj/06220355

Subjects:
Primary: 11M41
Secondary: 17B20, 40B05

Rights: Copyright © 2010 Mathematical Society of Japan

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Vol.62 • No. 2 • April, 2010
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