Opuscula Math. 35, no. 5 (2015), 567-594
http://dx.doi.org/10.7494/OpMath.2015.35.5.567

 
Opuscula Mathematica

Rigidity of monodromies for Appell's hypergeometric functions

Yoshishige Haraoka
Tatsuya Kikukawa

Abstract. For monodromy representations of holonomic systems, the rigidity can be defined. We examine the rigidity of the monodromy representations for Appell's hypergeometric functions, and get the representations explicitly. The results show how the topology of the singular locus and the spectral types of the local monodromies work for the study of the rigidity.

Keywords: rigidity, monodromy, arrangement of hyperplanes.

Mathematics Subject Classification: 33C65, 57M05.

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  • Yoshishige Haraoka
  • Kumamoto University, Department of Mathematics, Kumamoto 860-8555, Japan
  • Tatsuya Kikukawa
  • Kumamoto High School, Shin-Oe 1-8, Kumamoto 862-0972, Japan
  • Communicated by P.A. Cojuhari.
  • Received: 2014-02-28.
  • Revised: 2014-06-09.
  • Accepted: 2014-11-15.
  • Published online: 2015-04-27.
Opuscula Mathematica - cover

Cite this article as:
Yoshishige Haraoka, Tatsuya Kikukawa, Rigidity of monodromies for Appell's hypergeometric functions, Opuscula Math. 35, no. 5 (2015), 567-594, http://dx.doi.org/10.7494/OpMath.2015.35.5.567

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