A proof of the q-Macdonald-Morris conjecture for BC[n]
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Bibliographic Information
A proof of the q-Macdonald-Morris conjecture for BC[n]
（Memoirs of the American Mathematical Society, no. 516）
American Mathematical Society, 1994
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Note
"March 1994, volume 108, number 516 (first of 5 numbers)"
Includes bibliographical references (p. 79-80)
Description and Table of Contents
Description
Macdonald 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.
Table of Contents
Introduction 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.
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