Proof of the Q-Macdonald-Morris Conjecture for BC N
Seiten
1992
American Mathematical Society (Verlag)
978-0-8218-2552-5 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-2552-5 (ISBN)
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Uses a constant term formulation of Aomoto's argument to treat the $q$-Macdonald-Morris conjecture for the root system $BC_n$. This work gives some of the details for $C_n$ and $C_n^{/lor}$.
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.
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.
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.
| Erscheint lt. Verlag | 30.3.1994 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 198 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8218-2552-6 / 0821825526 |
| ISBN-13 | 978-0-8218-2552-5 / 9780821825525 |
| Zustand | Neuware |
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