Hypergeometric functions of type $BC$ and standard multiplicities
Abstract
We study the Heckman-Opdam hypergeometric functions associated to a root system of type 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 to spherical functions over homogeneous vector bundles on which are associated to certain small types.
Cite
@article{arxiv.2008.00337,
title = {Hypergeometric functions of type $BC$ and standard multiplicities},
author = {E. K. Narayanan and A. Pasquale},
journal= {arXiv preprint arXiv:2008.00337},
year = {2023}
}
Comments
The present paper subsumes and extends the results of the preprint arXiv:1705.00277. With respect to arXiv:2008.00337: Corrected Proposition 3.5. Some computations added in Appendix B