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Hypergeometric Functions of Type BC and Standard Multiplicities

Narayanan, EK and Pasquale, A (2022) Hypergeometric Functions of Type BC and Standard Multiplicities. In: International Mathematics Research Notices, 2022 (19). pp. 15111-15154.

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Official URL: https://doi.org/10.1093/imrn/rnab146


We study the Heckman–Opdam hypergeometric functions associated with a root system of type BC and a multiplicity function that is allowed to assume some nonpositive values (a standard multiplicity function). For such functions, we obtain positivity properties and sharp estimates that imply a characterization of the bounded hypergeometric functions. As an application, our results extend the 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 with certain small K-types.

Item Type: Journal Article
Publication: International Mathematics Research Notices
Publisher: Oxford University Press
Additional Information: The copyright for this article belongs to the Authors.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 15 Jun 2023 09:07
Last Modified: 15 Jun 2023 09:07
URI: https://eprints.iisc.ac.in/id/eprint/82002

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