IRREDUCIBILITY AND REDUCIBILITY OF LAURICELLA'  S SYSTEM OF DIFFERENTIAL EQUATIONS ED AND THE JORDAN-POCHHAMMER DIFFERENTIAL EQUATION EJP

Katsuhisa MIMACHI; Takeshi SASAKI

doi:10.2206/kyushujm.66.61

Kyushu Journal of Mathematics

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

IRREDUCIBILITY AND REDUCIBILITY OF LAURICELLA' S SYSTEM OF DIFFERENTIAL EQUATIONS E_D AND THE JORDAN-POCHHAMMER DIFFERENTIAL EQUATION E_JP

Katsuhisa MIMACHI, Takeshi SASAKI

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Keywords: Lauricella' s F_D, Jordan-Pochhammer equation, hypergeometric integrals, monodromy representations, irreducibility of the monodromy group

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2012 Volume 66 Issue 1 Pages 61-87

DOI https://doi.org/10.2206/kyushujm.66.61

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Abstract

Monodromy representations on the solution space of Lauricella' s system of differential equations E_D and the Jordan-Pochhammer differential equation E_JP are studied by using integrals of a multivalued function. We first establish the fact that any solution of E_D and any solution of E_JP are both expressed by the integrals of a multivalued function. Second, a necessary and sufficient condition for the irreducibility is given.

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