微分-差分算子与非不变元素的径向部分公式
Differential-difference operators and radial part formulas for non-invariant elements
摘要：
利用Cherednik算子和自然附着在G/K上的分次Hecke代数H，将黎曼对称空间G/K上的不变微分算子和K-不变函数的经典径向部分公式推广到非不变的情形.本文引入一个范畴C_{rad}，它的对象是一对（g_C，K）-模和一个H-模，它们满足与广义Chevalley限制定理和广义径向部分公式形式上相同的公理. G和H的表示论中的各种类似概念，如傅里叶变换和Opdam-Cherednik变换，都统一在C_{rad}中。我们构造了自然函子，它使H-模成为（g_C，K）-模，并具有与C_{rad}密切相关的一些泛性质.
英文摘要：
The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant cases by use of Cherednik operators and a graded Hecke algebra H naturally attached to G/K. We introduce a category C_{rad} whose object is a pair of a (g_C,K)-module and an H-module satisfying some axioms which are formally the same as the generalized Chevalley restriction theorem and the generalized radial part formula. Various pairs of analogous notions in the representation theories for G and H, such as the Helgason-Fourier transform and the Opdam-Cherednik transform, are unified in terms of C_{rad}. We construct natural functors which send an H-module to a (g_C,K)-module and have some universal properties intimately related to C_{rad}.
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