Tohoku Mathematical Journal
2006
March
SECOND SERIES VOL. 58, NO. 1

Tohoku Math. J.
58 (2006), 1-31

Title ON CONFLUENCES OF GENERAL HYPERGEOMETRIC SYSTEMS

Author Hironobu Kimura and Kyoichi Takano

(Received October 20, 2003, revised October 11, 2005)
Abstract. We extend the well-known results about the process of confluence for the Gauss hypergeometric differential equation to the case of general hypergeometric systems. We see that the process of confluence comes from the geometry of the set of regular elements of the Lie algebra of complex general linear group. As a consequence, we give a geometric and group-theoretic view on the process of confluence for classical special functions.

2000 Mathematics Subject Classification. Primary 33C70; Secondary 33C15.
Key words and phrases. ypergeometric system, confluence, regular element, stratification.

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