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arXiv · 2008.00337

Hypergeometric functions of type $BC$ and standard multiplicities

E. K. Narayanan·A. Pasquale
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Abstract

We study the Heckman-Opdam hypergeometric functions associated to a root system of type $BC$ and a multiplicity function which is allowed to assume some non-positive values (a standard multiplicity function). For such functions, we obtain positivity properties and sharp estimates which imply a characterization of the bounded hypergeometric functions. As an application, our results extend known properties of Harish-Chandra's spherical functions on Riemannian symmetric spaces of the non-compact type $G/K$ to spherical functions over homogeneous vector bundles on $G/K$ which are associated to certain small $K-$types.

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BibTeXRIS

E. K. Narayanan, A. Pasquale. 2020-08-01. Hypergeometric functions of type $BC$ and standard multiplicities. https://doi.org/10.1093/imrn%2Frnab146

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