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The $ A_\ell$ and $ C_\ell$ Bailey transform and lemma


Authors: Stephen C. Milne and Glenn M. Lilly
Journal: Bull. Amer. Math. Soc. 26 (1992), 258-263
MSC (2000): Primary 33D70; Secondary 05A19, 11B65, 11P83
MathSciNet review: 1118702
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Abstract: We announce a higher-dimensional generalization of the Bailey Transform, Bailey Lemma, and iterative "Bailey chain" concept in the setting of basic hypergeometric series very well-poised on unitary $ {A_\ell }$ or symplectic $ {C_\ell }$ groups. The classical case, corresponding to $ {A_1}$ or equivalently $ {\text{U}}(2)$, contains an immense amount of the theory and application of one-variable basic hypergeometric series, including elegant proofs of the Rogers-Ramanujan-Schur identities. In particular, our program extends much of the classical work of Rogers, Bailey, Slater, Andrews, and Bressoud.


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DOI: http://dx.doi.org/10.1090/S0273-0979-1992-00268-9
Article copyright: © Copyright 1992 American Mathematical Society