Memoirs of the American Mathematical Society 1994; 80 pp; softcover Volume: 108 ISBN10: 0821825526 ISBN13: 9780821825525 List Price: US$39 Individual Members: US$23.40 Institutional Members: US$31.20 Order Code: MEMO/108/516
 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 \(q\)MacdonaldMorris 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. Readership Research mathematicians. 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 \(q\)MacdonaldMorris conjecture for \(B_n,B_n^\lor ,C_n,C_n^\lor\) and \(D_n\)
 Conclusion
