A formula for the hypergeometric function of type $BC_n$
Nobukazu shimeno
TL;DR
This paper generalizes formulas for hypergeometric functions related to root systems of type BC_n, extending previous work on invariant differential operators and spherical functions on complex Grassmann manifolds.
Contribution
It introduces new formulas for hypergeometric functions of type BC_n under specific multiplicity conditions, broadening the understanding of these functions in harmonic analysis.
Findings
Generalized Berezin and Karpelevic formulas to BC_n hypergeometric functions
Extended invariant differential operator analysis to new root systems
Provided explicit formulas under specific multiplicity conditions
Abstract
Formulae of Berezin and Karpelevic 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 system of type under condition that the multiplicity of the middle roots is zero or one.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Nonlinear Waves and Solitons · Holomorphic and Operator Theory