Some applications of hypergeometric shift operators
Some applications of hypergeometric shift operators
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DOI：
10.1007/bf01388841
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发表时间：
1989-02
影响因子：
3.1
通讯作者：
E. Opdam
中科院分区：
文献类型：
--
作者：
E. Opdam
在本文中，我们将讨论所谓的超几何移位算子存在定理的一些非常自然的结果，这些定理在[02]（定理3.6）中得到了证明。顾名思义，这些移位算子在与根系相关的几个变量的广义超几何函数理论中发挥着重要作用，如论文 [HO]、[HI、[O1] 和 [02] 中所阐述的那样。上述存在性定理基于 Heckman 论文 [H] 的主要结果，该论文指出，某个二阶微分算子 L 与根系 R 和 R 上的重数函数 ~ 相关联，具有某些特殊的特征函数，这些特征函数是具有指定单向行为的 Niisson 类函数。据我们目前所知，赫克曼结果的基本原理是所谓的黎曼-希尔伯特对应关系（由 P. Deligne [D] 获得的形式）。为了让读者了解什么是移位运算符，我们看一下最简单的示例，即 R= BC1 的情况。一般理论归结为普通超几何函数 d 的理论
In this paper we will discuss some very natural consequences of the existence theorem of so called hypergeometric shift operators, which is proved in [02](Theorem 3.6). These shift operators play a role, as their name indicates, in the theory of generalized hypergeometric functions of several variables associated with root systems as developed in the papers [HO],[HI,[O1] and [02]. The above mentioned existence theorem is based on the main result of Heckman's paper [H], which states that a certain second order differential operator L, associated with a root system R and a multiplicity function~ on R, has certain special eigenfunctions that are Niisson class functions with a prescribed monodromy behaviour. The underlying principle in Heckman's result is, as far as we understand at this moment, the so called Riemann-Hilbert correspondence (in the form obtained by P. Deligne [D]). In order to give the reader an idea what shift operators are we take a look at the simplest possible example, namely the case where R= BC1. The general theory boils down to the theory of the ordinary hypergeometric function d