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October 2019 Irreducibility of the monodromy representation of Lauricella's $F_C$
Yoshiaki GOTO, Keiji MATSUMOTO
Hokkaido Math. J. 48(3): 489-512 (October 2019). DOI: 10.14492/hokmj/1573722015

Abstract

Let $E_C$ be the hypergeometric system of differential equations satisfied by Lauricella's hypergeometric series $F_C$ of $m$ variables. This system is irreducible in the sense of $D$-modules if and only if $2^{m+1}$ non-integral conditions for parameters are satisfied. We find a linear transformation of the classically known $2^m$ solutions so that the transformed ones always form a fundamental system of solutions under the irreducibility conditions. By using this fundamental system, we give an elementary proof of the irreducibility of the monodromy representation of $E_C$. When one of the conditions is not satisfied, we specify a non-trivial invariant subspace, which implies that the monodromy representation is reducible in this case.

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Yoshiaki GOTO. Keiji MATSUMOTO. "Irreducibility of the monodromy representation of Lauricella's $F_C$." Hokkaido Math. J. 48 (3) 489 - 512, October 2019. https://doi.org/10.14492/hokmj/1573722015

Information

Published: October 2019
First available in Project Euclid: 14 November 2019

zbMATH: 07145327
MathSciNet: MR4031249
Digital Object Identifier: 10.14492/hokmj/1573722015

Subjects:
Primary: 32S40, 33C65

Rights: Copyright © 2019 Hokkaido University, Department of Mathematics

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Vol.48 • No. 3 • October 2019
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