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A Proof of the $q$-Macdonald-Morris Conjecture for $BC_n$
Kevin W. J. Kadell
出版American Mathematical Soc., 1994
主題Mathematics / CalculusMathematics / Functional AnalysisMathematics / Topology
ISBN08218255269780821825525
URLhttp://books.google.com.hk/books?id=oX_UCQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋Macdonald and Morris gave a series of constant term [italic]q-conjectures associated with root systems. Selberg evaluated a multivariable beta-type integral which plays an important role in the theory of constant term identities associated with root systems. K. Aomoto recently gave a simple and elegant proof of a generalization of Selberg's integral. Kadell extended this proof to treat Askey's conjectured [italic]q-Selberg integral, which was proved independently by Habsieger. We use a constant term formulation of Aomoto's argument to treat the [italic]q-Macdonald-Morris conjecture for the root system [italic capitals]BC[subscript italic]n. We show how to obtain the required functional equations using only the q-transportation theory for [italic capitals]BC[subscript italic]n.