Abstract

Formulae of Berezin and Karpelevič for the radial parts of invariant differential operators and the spherical function on a complex Grassmann manifold are generalized to the hypergeometric functions associated with root systems of type BC_n under the condition that the multiplicity of the middle roots is zero or one.

Keywords

hypergeometric function, Berezin, Karpelevic, Heckman, Opdam, determinant

Mathematical Subject Classification

Primary: 33C67

Secondary: 43A90

Authors