Mathematical Sciences: Hypergeometric Series Very-Well- Poised on Semisimple Lie Algebras and Multivariate Orthogonal Polynomials

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This award supports the research on multivariable hyper- geometric series of Professor Robert Gustafson of Texas A & M University. Dr. Gustafson has proposed to develop the theory of hypergeometric series that are very well poised on semisimple Lie algebras, as well as the corresponding theory of beta and Mellin- Barnes integrals on compact Lie groups and the associated Lie algebras. In addition, he plans to relate this theory to the families of orthogonal polynomials associated to root systems, recently defined by Macdonald. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.