Tohoku Mathematical Journal
2017
December
SECOND SERIES VOL. 69, NO. 4

Tohoku Math. J.
69 (2017), 547-570

Title MONODROMY REPRESENTATIONS OF HYPERGEOMETRIC SYSTEMS WITH RESPECT TO FUNDAMENTAL SERIES SOLUTIONS

Author Keiji Matsumoto

(Received May 15, 2015, revised November 9, 2015)
Abstract. We study the monodromy representation of the generalized hypergeometric differential equation and that of Lauricella's $F_C$ system of hypergeometric differential equations. We use fundamental systems of solutions expressed by the hypergeometric series. We express non-diagonal circuit matrices as reflections with respect to root vectors with all entries 1. We present a simple way to obtain circuit matrices.

Mathematics Subject Classification. Primary 32S40; Secondary 34M35, 33C20, 33C65.
Key words and phrases. Monodromy representation, hypergeometric functions.

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