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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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The $A_\ell$ and $C_\ell$ Bailey transform and lemma
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by Stephen C. Milne and Glenn M. Lilly PDF
Bull. Amer. Math. Soc. 26 (1992), 258-263 Request permission

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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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 26 (1992), 258-263
  • MSC (2000): Primary 33D70; Secondary 05A19, 11B65, 11P83
  • DOI: https://doi.org/10.1090/S0273-0979-1992-00268-9
  • MathSciNet review: 1118702