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Hypergeometric Functions of Type BC and Standard Multiplicities
International Mathematics Research Notices ( IF 1 ) Pub Date : 2021-05-11 , DOI: 10.1093/imrn/rnab146
Eravimangalam Krishnan Narayanan 1 , Angela Pasquale 2
Affiliation  

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.

中文翻译:

BC 型和标准多重性的超几何函数

我们研究了与 $BC$ 类型的根系统相关的 Heckman-Opdam 超几何函数和允许假设一些非正值的多重函数(标准多重函数)。对于这样的函数,我们获得了暗示有界超几何函数特征的正性属性和尖锐估计。作为一个应用,我们的结果将 Harish-Chandra 在非紧致类型 $G/K$ 的黎曼对称空间上的球函数的已知性质扩展到 $G/K$ 上的齐次向量丛上的球函数,这与某些相关联小的 $K$ 类型。
更新日期:2021-05-11
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