Some applications of hypergeometric shift operators. (English) Zbl 0696.33006

The author gives proofs of the formulae defining some properties of certain polynomial functions associated with root systems of Lie algebras. These formulae were earlier given as conjectures both by the author and others. The results obtained involve the search of the constant term of the Laurent polynomial, the evaluation of the Jacobi polynomial at the identity element in terms of Harish-Chandra’s c- function, the structure of the Bernstein-Sato polynomial. These results are obtained as consequences of the existence theorem of shift operators which play an important role in the theory of generalized hypergeometric functions of several variables associated with root systems.
Reviewer: A.V.Rosenblyum


33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
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