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Root systems and hypergeometric functions. IV. (English) Zbl 0669.33008

In three preceding papers (for part III, see the preceding review) the author and G. J. Heckmann developed a theory on multivariable hypergeometric functions associated with arbitrary root systems. In this paper the author makes further investigation on the structure of this class of functions, especially on the analytic continuation. Based on this investigation the author proves the complete integrability of three classical Hamiltonian systems that are connected with root systems.
Reviewer: G.Tu

MSC:

33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
17B20 Simple, semisimple, reductive (super)algebras
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References:

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