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

2010/04/01 by Kohji Matsumoto, Yasushi Komori, Hirofumi Tsumura · 2 citations
Chemistry · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebra over a field #Arithmetic zeta function #Computer science #Continuation #Lie algebra #Mathematics #Molecular spectroscopy and chirality #Order (exchange) #Pure mathematics #Riemann zeta function #Simple (philosophy) #Type (biology) #math.NT #msc:11M06 #msc:11M32

paper · pdf · doi:10.2969/jmsj/06220355

published as J. Math. Soc. Japan 67 (2015), 383-406 · 23 pages

openalex publication_date 2010/04/01 · arxiv created 2014/12/22 · arxiv updated 2016/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Decompositions of Rational Convex Polytopes
• On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III

Cited by

• Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems
• A study on multiple zeta values from the viewpoint of zeta-functions of root systems
• ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS V