Mathematical Sciences: Research in Generalized Special Functions

有一长串数学函数（贝塞尔函数、超几何函数等）被称为特殊函数，因为它们在应用中无处不在，经常作为微分方程的解遇到。这个项目的研究集中在超几何函数的类似物上，其中的参数是一个矩阵，而不是一个实数或复数。一般线性群的表示理论在这一研究中起着重要的作用，因为广义超几何函数的定义域可以被认为具有该群的某个商。有一个高度接触多元统计，理查兹教授的原始研究领域，并与当前的代数学者非常感兴趣的组合问题。

There is a long list of mathematical functions (Bessel, hypergeometric, and the like) called special because of their omnipresence in applications, where they are often encountered as solutions to differential equations. The research in this project centers on analogues of the hypergeometric functions in which the argument is a matrix, rather than a real or complex number. The representation theory of the general linear group plays a major role in this investigation, because the generalized hypergeometric functions can be thought of as having for their domain of definition a certain quotient of that group. There is a high degree of contact with multivariate statistics, Professor Richards' original research area, and with combinatorial problems of great current interest to algebraists.