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Reductibility and irreducibility of the Gauss-Manin system associated with a Selberg type integral

Published online by Cambridge University Press:  22 January 2016

Katsuhisa Mimachi
Katsuhisa Mimachi*
Affiliation:
Department of Mathematics, Faculty of Science, Kyushu University, Hakozaki, Fukuoka 812, Japan
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Consider the function with variables z1…,zm

where υ and λj (j = 1,…,m) are complex numbers and.Г is a suitably chosen integral domain. In case m = 2, if we set [z1 z2]n as Г, it is the Selberg integral [22]. Our function can be regarded as an extention of it; so we may call (0.1) a Selberg type integral It is known that (0.1) satisfies a Gauss-Manin system, i.e. a system of rationally holonomic differential equations [3], [21].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 132 , December 1993 , pp. 43 - 62
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

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