论文标题
类型$ bc $和标准多重性的超几何功能
Hypergeometric functions of type $BC$ and standard multiplicities
论文作者
论文摘要
我们研究了与类型$ bc $的根系和多重功能相关的Heckman-Opdam超几何函数，该功能允许假设某些非阳性值（标准的多样性函数）。对于此类功能，我们获得了阳性特性和尖锐的估计，这意味着有界超几何函数的表征。作为应用程序，我们的结果将Harish-Chandra的球形功能扩展到了非紧密的$ G/K $的Riemannian对称空间上的已知属性，以在$ G/k $上的均质矢量包上的球形功能，这些功能与某些小型$ k-$相关。
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.
