This research will concentrate on three areas: the completion of the proof of the q-MacDonald-Morris constant term conjectures, combinatorial proofs of some results related to the B root system and the q-Selberg polynomials. The basic theme is the extension of techniques which are successful for the A root system to the other root systems. Kadell has extended Aomoto's proof of Selberg's integral to the q-case and proved the q- MacDonald-Morris conjecture for BC root system. This should extend to treat the remaining root systems. A number of results for Schur functions related to the A root systems have been proven combinatorially. Kadell will attack some related problems associated with the B root system. Finally the q-Selberg polynomials extend the Schur functions, the little q-Jacobi polynomials and the zonal polynomials and it is hoped that a theory of these polynomials, including a combinatorial representation, can be based on a conjectured orthogonality relation. This research focuses on the theory of combinatorial identities, an important subject that combines combinatorial ideas with deep problems and techniques from algebra and analysis. The subject has recently become even more important with the discovery with important ties to physics. The MacDonald conjectures and their many variants have been the central focal point of this area for years. Kadell is making significant progress on these deep problems and will continue to make exciting contributions during this research.
