Proof of the Q-Macdonald-Morris Conjecture for BC N (Memoirs of the American Mathematical Society)

Proof of the Q-Macdonald-Morris Conjecture for BC N (Memoirs of the American Mathematical Society)

By: Kevin W. J. Kadell (author), Rolf Schon (author)Paperback

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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.

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.

Product Details

  • ISBN13: 9780821825525
  • Format: Paperback
  • Number Of Pages: 63
  • ID: 9780821825525
  • ISBN10: 0821825526

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