| eBook ISBN: | 978-1-4704-0093-4 |
| Product Code: | MEMO/108/516.E |
| List Price: | $39.00 |
| MAA Member Price: | $35.10 |
| AMS Member Price: | $23.40 |
| eBook ISBN: | 978-1-4704-0093-4 |
| Product Code: | MEMO/108/516.E |
| List Price: | $39.00 |
| MAA Member Price: | $35.10 |
| AMS Member Price: | $23.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 108; 1994; 80 ppMSC: Primary 17
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.
ReadershipResearch mathematicians.
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Table of Contents
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Chapters
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1. Introduction
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2. Outline of the proof and summary
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3. The simple roots and reflections of $B_n$ and $C_n$
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4. The $q$-engine of our $q$-machine
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5. Removing the denominators
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6. The $q$-transportation theory for $BC_n$
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7. Evaluation of the constant terms $A$, $E$, $K$, $F$ and $Z$
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8. $q$-analogues of some functional equations
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9. $q$-transportation theory revisited
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10. A proof of Theorem 4
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11. The parameter $r$
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12. The $q$-Macdonald-Morris conjecture for $B_n$, $B^\vee _n$, $C_n$, $C^\vee _n$ and $D_n$
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13. Conclusion
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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.
Research mathematicians.
-
Chapters
-
1. Introduction
-
2. Outline of the proof and summary
-
3. The simple roots and reflections of $B_n$ and $C_n$
-
4. The $q$-engine of our $q$-machine
-
5. Removing the denominators
-
6. The $q$-transportation theory for $BC_n$
-
7. Evaluation of the constant terms $A$, $E$, $K$, $F$ and $Z$
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8. $q$-analogues of some functional equations
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9. $q$-transportation theory revisited
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10. A proof of Theorem 4
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11. The parameter $r$
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12. The $q$-Macdonald-Morris conjecture for $B_n$, $B^\vee _n$, $C_n$, $C^\vee _n$ and $D_n$
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13. Conclusion
