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

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Abstract

This is a continuation of our previous result, in which properties of multiple zeta-functions associated with simple Lie algebras of <i>A</i><sub><i>r</i></sub> 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 <i>B</i><sub><i>r</i></sub>, <i>C</i><sub><i>r</i></sub>, and <i>D</i><sub><i>r</i></sub> types.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 62(2), 355-394, 2010-04-01

    The Mathematical Society of Japan

References:  22

Codes

  • NII Article ID (NAID)
    10026999060
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    10658814
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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