Mathematical Sciences: Research in Generalized Special Functions

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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.