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OverviewMacdonald and Morris gave a series of constant term $q$-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. Aomoto recently gave a simple and elegant proof of a generalization of Selberg's integral. Kadell extended this proof to treat Askey's conjectured $q$-Selberg integral, which was proved independently by Habsieger. This monograph uses a constant term formulation of Aomoto's argument to treat the $q$-Macdonald-Morris conjecture for the root system $BC_n$. The $B_n$, $B_n^{\lor}$, and $D_n$ cases of the conjecture follow from the theorem for $BC_n$. Some of the details for $C_n$ and $C_n^{\lor}$ are given. This illustrates the basic steps required to apply methods given here to the conjecture when the reduced irreducible root system $R$ does not have miniscule weight. Full Product DetailsAuthor: Kevin W. J. Kadell , Rolf SchonPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 516 Weight: 0.198kg ISBN: 9780821825525ISBN 10: 0821825526 Pages: 63 Publication Date: 30 March 1994 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsIntroduction Outline of the proof and summary The simple roots and reflections of $B_n$ and $C_n$ The $q$-engine of our $q$-machine Removing the denominators The $q$-transportation theory for $BC_n$ Evaluation of the constant terms $A,E,K,F$ and $Z$ $q$-analogues of some functional equations $q$-transportation theory revisited A proof of Theorem 4 The parameter $r$ The $q$-Macdonald-Morris conjecture for $B_n,B_n^\lor,C_n,C_n^\lor$ and $D_n$ Conclusion.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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