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Root systems and hypergeometric functions. III. (English) Zbl 0669.33007
In parts I, II [ibid. 64, 329-352, 353-373 (1987; Zbl 0656.17006, Zbl 0656.17007)] the author and G. J. Heckman studied a class of differential equations associated with a root system R, the solutions of these equations are then used to introduce multivariable hypergeometric functions. In their construction they made essential use of the hypothesis that the so-called Harish-Chandra homomorphism is an isomorphism onto.
This third part under review gives a proof of that fact when R is a root system of type \(G_ 2\). This result gives a possibility for constructing the hypergeometric function associated with arbitrary root systems.
Reviewer: G.Tu

MSC:
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
17B20 Simple, semisimple, reductive (super)algebras
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References:
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