Mathematical Sciences: Research in Generalized Special Functions

有一长串数学函数（贝塞尔， 超几何等）称为特殊的，因为他们的 在应用程序中无处不在，在这些应用程序中， 解微分方程。本项目的研究 中心的超几何函数的类似物，其中， 参数是一个矩阵，而不是一个真实的或复数。的 一般线性群的表示理论在 在这次调查中的作用，因为广义的 超几何函数可以被认为具有 定义域是该群的某个商。有一个 与多元统计学的高度接触，教授 理查兹的原始研究领域，并与组合问题 目前代数学家非常感兴趣。

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.