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On contiguity relations of the confluent hypergeometric systems. (English) Zbl 0798.33009
The generalized confluent hypergeometric systems have been formulated in the earlier papers [I. M. Gel’fand, V. S. Retakh and V. V. Serganova, Generalized Airy functions, Schubert cells, and Jordan groups, Sov. Math., Dokl. 37, 8-12 (1988; Zbl 0699.33012)] and H. Kimura, Y. Haraoka and K. Takano, The generalized confluent hypergeometric functions, Proc. Japan Acad., Ser. A 68, No. 9, 290-295 (1992; Zbl 0773.33004)]. They are obtained from the generalized hypergeometric systems defined on Grassmannian manifolds. This paper deals with the symmetry of the confluent hypergeometric system by representing them as contiguity relations that hold among solutions with different parameters.
Reviewer: T.Sasaki (Kobe)

MSC:
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
17B66 Lie algebras of vector fields and related (super) algebras
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