MONODROMY REPRESENTATIONS ASSOCIATED WITH APPELL' S HYPERGEOMETRIC FUNCTION F1 USING INTEGRALS OF A MULTIVALUED FUNCTION

Katsuhisa MIMACHI; Takeshi SASAKI

doi:10.2206/kyushujm.66.89

Kyushu Journal of Mathematics

Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116

MONODROMY REPRESENTATIONS ASSOCIATED WITH APPELL' S HYPERGEOMETRIC FUNCTION F₁ USING INTEGRALS OF A MULTIVALUED FUNCTION

Katsuhisa MIMACHI, Takeshi SASAKI

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Keywords: hypergeometric integral, Appell' s hypergeometric function F₁, monodromy representation, finite reducible monodromy group

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2012 Volume 66 Issue 1 Pages 89-114

DOI https://doi.org/10.2206/kyushujm.66.89

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Abstract

Monodromy representations on the solution space of Appell' s system of differential equations E₁ are studied by using integrals of a multivalued function. In particular, we realize the representations in the reducible cases and give a complete list of finite reducible representations.

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